What is Vector? The meaning of the word “Vector” in popular dictionaries and encyclopedias, examples of the use of the term in everyday life.

Vector of Constructive Tension – Philosophical Dictionary

A necessary element of constructive tension that determines the orientation, direction of reproduction, personal culture, personality, its activities, communities at all stages of the social whole; brigades, enterprises, departments, etc. reproduction of subcultures corresponding to communities. V.K.S. is a necessary element of any dual opposition as an indicator of value orientation, built into any reproductive activity of the subject. Thus, not only is there a division of reality into good and evil, but also the need for the subject to strive for good and avoid evil. Dual opposition carries within itself positive and negative, direct and reverse V.K. By mastering the corresponding (sub)cultures, the individual thereby acquires a certain orientation in the fight against disorganization. Each of the cells of society is characterized by a certain specific orientation that is opposed to entropy and disorganization. In this regard, the most important problem in any society is the degree of coincidence of vectors at different levels of society, the degree of coincidence of V.K.N. individuals and organizations, teams and enterprises, etc. Any community can work normally if its inherent V.K. coincides with, does not significantly diverge from V.K.N. its members recreating its people. Otherwise, a sociocultural contradiction arises, giving rise to disorganization, which threatens both the growth of innovations above the level of novelty acceptable in a given subculture, and a decrease in social energy below the lower threshold.

Vector M. – Explanatory Dictionary by Efremova

1. A straight segment, characterized by a numerical value and a certain direction.

Expected Return Vector – Economic dictionary

a vector of numbers corresponding to expected returns for a given set of securities.

Vector of Ranks – Sociological Dictionary

– vector statistics constructed from a random vector of observations X = (X1, ... ,Xn) (see Vector), the components of which are obtained as follows. If all Xt are different, then the components of V.r. are natural numbers from 1 to n: in place of each Xi there is a number expressing the number of such components of the vector Xi, the value of which is less than the value of Xi. In other words, in the place of the largest Xi there is the number n, in the place of the next largest (in descending order) - (n-1), etc. In the place of the smallest there is 1. If certain X. are equal to each other , then V.r. is constructed as follows: the largest X is assigned rank n, the next largest is assigned rank (n-1), etc. until, after assigning rank (n-k), equal Xi are encountered. Let these be Xkl,...,Xkl. We assign a rank to each of them. The next largest Xkl 1 we assign a rank n-(to l 1), if it is not equal to any other component of X, and the rank of Yu.N. Tolstov

State Vector –

same as wave function.

Vectorcardiography – Psychological Dictionary

(vectorcardiography) - see Electrocardiography.

Vectorcardiography – Psychological Encyclopedia

Vectorcardiography – Medical dictionary

see Electrocardiography.

Vectormeter – Big Encyclopedic Dictionary

(from vector and...meter) - a device for measuring currents, voltages and phases of alternating current.

Vectormeter M. – Explanatory Dictionary by Efremova

1. Electrical appliance for measuring voltage or strength and phase of alternating current.

Vector Diagram – Big Encyclopedic Dictionary

graphical representation of the values ​​of physical quantities that change according to a harmonic law, and the relationships between them in the form of vectors. Used in calculations in electrical engineering, acoustics, optics, etc.

Vector Psychology – Sociological Dictionary

See FIELD THEORY.

Vector Psychology – Psychological Dictionary

See the discussion of Lewin's theory in the article vector(1).

Vector Psychology – Psychological Encyclopedia

Vector Calculus – Big Encyclopedic Dictionary

branch of mathematics in which operations with supervectors are studied. includes vector algebra and vector analysis. The rules of vector algebra reflect the properties of actions by supervector quantities. For example, the sum of vectors a and b is a vector going from the beginning of vector a to the end of vector b, provided that the beginning of vector b is applied to the end of vector a; this rule is related to the rule of addition of forces or velocities (see Parallelogram of forces). In vector calculus, two types of vector multiplication are established (see Dot product, Vector product). If i, j, k are three mutually perpendicular unit vectors in space, then any vector a can be uniquely represented in the form a=a1i+a2j+a3k. The numbers a1, a2, a3 are called components (coordinates) of vector a. Vector analysis is based on the operations of differentiation and integration of vector functions.

Vector Field – Big Encyclopedic Dictionary

a region at each point P of which a vector a(P) is specified. Many physical phenomena and processes lead to the concept of a vector field (for example, the velocity vectors of particles of a moving fluid at each moment of time form a vector field).

Vector Product – Big Encyclopedic Dictionary

vector a to vector b - vector p = VECTOR SPACE - a mathematical concept that generalizes the concept of the set of all vectors of a 3-dimensional space to the case of an arbitrary number of dimensions.

Vector Approach to Psychotherapy – Psychological Dictionary

(vector approach to psychotherapy) V. p. p. postulates that the entire variety of therapies is essentially distributed along 6 main lines. vectors, or modalities, indicating the direction of growth. Choosing one of many therapeutic methods, mainly On these vectors, the eclectically oriented therapist can achieve highly effective balanced therapeutic integration, as well as gain freedom to express their personal preferences and talents. Below is the classification. therapy methods based on these vectors. 1. Rational vector, characterized by insight, expansion of awareness and learning: a) psychoan; b) rational-emotive therapy; c) transactional analysis; d) behavioral therapy. 2. Neuromuscular vector, characterized by muscle tension, muscle relaxation and movement, accompanied by changes in breathing and release of emotions: a) Reichian therapy; b) bioenergy; c) rolfing; d) Alexander's method; e) Feldenkrais method; e) dance therapy. 3. Interpersonal vector, characterized by relationships between people: a) groups of meetings; b) psychodrama; c) joint family therapy; d) Gestalt therapy. 4. Vector of fantasy, characterized by intrapersonal experience when external stimulation is turned off: a) hypnotherapy; b) psychosynthesis; c) guided daydreams. 5. Transpersonal vector, characterized by the transcendence of the closed state of consciousness of the individual: a) spiritual healing; b) parapsychological phenomena; c) Jungian psychology; d) meditation. 6. Biochemical vector, characterized by chemical changes in the body that have internal or external origin: a) orthomolecular therapy; b) carbogen; c) dietary procedures and exercises; d) psychedelic and psycholytic drug therapy; e) sedatives, stimulants and tranquilizers. See also Innovative psychotherapies, Methods of psychotherapy by P. Bindrim

Finally, I got my hands on this vast and long-awaited topic. analytical geometry. First, a little about this section of higher mathematics... Surely you now remember a school geometry course with numerous theorems, their proofs, drawings, etc. What to hide, an unloved and often obscure subject for a significant proportion of students. Analytical geometry, oddly enough, may seem more interesting and accessible. What does the adjective “analytical” mean? Two cliched mathematical phrases immediately come to mind: “graphical solution method” and “analytical solution method.” Graphical method, of course, is associated with the construction of graphs and drawings. Analytical same method involves solving problems mainly through algebraic operations. In this regard, the algorithm for solving almost all problems of analytical geometry is simple and transparent; often it is enough to carefully apply the necessary formulas - and the answer is ready! No, of course, it won’t be possible to do this without drawings at all, and besides, for a better understanding of the material, I will try to cite them beyond the need.

The newly opened course of lessons on geometry does not pretend to be theoretically complete; it is focused on solving practical problems. I will include in my lectures only what, from my point of view, is important in practical terms. If you need more complete help on any subsection, I recommend the following quite accessible literature:

1) A thing that, no joke, several generations are familiar with: School textbook on geometry, authors – L.S. Atanasyan and Company. This school locker room hanger has already gone through 20 (!) reprints, which, of course, is not the limit.

2) Geometry in 2 volumes. Authors L.S. Atanasyan, Bazylev V.T.. This is literature for high school, you will need first volume. Rarely encountered tasks may fall out of my sight, and the tutorial will be of invaluable help.

Both books can be downloaded for free online. In addition, you can use my archive with ready-made solutions, which can be found on the page Download examples in higher mathematics.

Among the tools, I again propose my own development - software package in analytical geometry, which will greatly simplify life and save a lot of time.

It is assumed that the reader is familiar with basic geometric concepts and figures: point, line, plane, triangle, parallelogram, parallelepiped, cube, etc. It is advisable to remember some theorems, at least the Pythagorean theorem, hello to repeaters)

And now we will consider sequentially: the concept of a vector, actions with vectors, vector coordinates. I recommend reading further the most important article Dot product of vectors, and also Vector and mixed product of vectors. A local task - Division of a segment in this respect - will also not be superfluous. Based on the above information, you can master equation of a line in a plane With simplest examples of solutions, which will allow learn to solve geometry problems. The following articles are also useful: Equation of a plane in space, Equations of a line in space, Basic problems on a straight line and a plane, other sections of analytical geometry. Naturally, standard tasks will be considered along the way.

Vector concept. Free vector

First, let's repeat the school definition of a vector. Vector called directed a segment for which its beginning and end are indicated:

In this case, the beginning of the segment is the point, the end of the segment is the point. The vector itself is denoted by . Direction is essential, if you move the arrow to the other end of the segment, you get a vector, and this is already completely different vector. It is convenient to identify the concept of a vector with the movement of a physical body: you must agree, entering the doors of an institute or leaving the doors of an institute are completely different things.

It is convenient to consider individual points of a plane or space as the so-called zero vector. For such a vector, the end and beginning coincide.

!!! Note: Here and further, you can assume that the vectors lie in the same plane or you can assume that they are located in space - the essence of the material presented is valid for both the plane and space.

Designations: Many immediately noticed the stick without an arrow in the designation and said, there’s also an arrow at the top! True, you can write it with an arrow: , but it is also possible the entry that I will use in the future. Why? Apparently, this habit developed for practical reasons; my shooters at school and university turned out to be too different-sized and shaggy. In educational literature, sometimes they don’t bother with cuneiform writing at all, but highlight the letters in bold: , thereby implying that this is a vector.

That was stylistics, and now about ways to write vectors:

1) Vectors can be written in two capital Latin letters:
and so on. In this case, the first letter Necessarily denotes the beginning point of the vector, and the second letter denotes the end point of the vector.

2) Vectors are also written in small Latin letters:
In particular, our vector can be redesignated for brevity by a small Latin letter.

Length or module a non-zero vector is called the length of the segment. The length of the zero vector is zero. Logical.

The length of the vector is indicated by the modulus sign: ,

We will learn how to find the length of a vector (or we will repeat it, depending on who) a little later.

This was basic information about vectors, familiar to all schoolchildren. In analytical geometry, the so-called free vector.

To put it simply - the vector can be plotted from any point:

We are accustomed to calling such vectors equal (the definition of equal vectors will be given below), but from a purely mathematical point of view, they are the SAME VECTOR or free vector. Why free? Because in the course of solving problems, you can “attach” this or that vector to ANY point of the plane or space you need. This is a very cool feature! Imagine a vector of arbitrary length and direction - it can be “cloned” an infinite number of times and at any point in space, in fact, it exists EVERYWHERE. There is such a student saying: Every lecturer gives a damn about the vector. After all, it’s not just a witty rhyme, everything is mathematically correct - the vector can be attached there too. But don’t rush to rejoice, it’s the students themselves who often suffer =)

So, free vector- This many identical directed segments. The school definition of a vector, given at the beginning of the paragraph: “A directed segment is called a vector...”, implies specific a directed segment taken from a given set, which is tied to a specific point in the plane or space.

It should be noted that from the point of view of physics, the concept of a free vector is generally incorrect, and the point of application of the vector matters. Indeed, a direct blow of the same force on the nose or forehead, enough to develop my stupid example, entails different consequences. However, unfree vectors are also found in the course of vyshmat (don’t go there :)).

Actions with vectors. Collinearity of vectors

A school geometry course covers a number of actions and rules with vectors: addition according to the triangle rule, addition according to the parallelogram rule, vector difference rule, multiplication of a vector by a number, scalar product of vectors, etc. As a starting point, let us repeat two rules that are especially relevant for solving problems of analytical geometry.

The rule for adding vectors using the triangle rule

Consider two arbitrary non-zero vectors and :

You need to find the sum of these vectors. Due to the fact that all vectors are considered free, we set aside the vector from end vector:

The sum of vectors is the vector. For a better understanding of the rule, it is advisable to put a physical meaning into it: let some body travel along the vector , and then along the vector . Then the sum of vectors is the vector of the resulting path with the beginning at the departure point and the end at the arrival point. A similar rule is formulated for the sum of any number of vectors. As they say, the body can go its way very lean along a zigzag, or maybe on autopilot - along the resulting vector of the sum.

By the way, if the vector is postponed from started vector, then we get the equivalent parallelogram rule addition of vectors.

First, about collinearity of vectors. The two vectors are called collinear, if they lie on the same line or on parallel lines. Roughly speaking, we are talking about parallel vectors. But in relation to them, the adjective “collinear” is always used.

Imagine two collinear vectors. If the arrows of these vectors are directed in the same direction, then such vectors are called co-directed. If the arrows point towards different sides, then the vectors will be opposite directions.

Designations: collinearity of vectors is written with the usual parallelism symbol: , while detailing is possible: (vectors are co-directed) or (vectors are oppositely directed).

The work a non-zero vector on a number is a vector whose length is equal to , and the vectors and are co-directed at and oppositely directed at .

The rule for multiplying a vector by a number is easier to understand with the help of a picture:

Let's look at it in more detail:

1) Direction. If the multiplier is negative, then the vector changes direction to the opposite.

2) Length. If the multiplier is contained within or , then the length of the vector decreases. So, the length of the vector is half the length of the vector. If the modulus of the multiplier is greater than one, then the length of the vector increases at times.

3) Please note that all vectors are collinear, while one vector is expressed through another, for example, . The reverse is also true: if one vector can be expressed through another, then such vectors are necessarily collinear. Thus: if we multiply a vector by a number, we get collinear(relative to the original) vector.

4) The vectors are co-directional. Vectors and are also co-directed. Any vector of the first group is oppositely directed with respect to any vector of the second group.

Which vectors are equal?

Two vectors are equal if they are in the same direction and have the same length. Note that codirectionality implies collinearity of vectors. The definition would be inaccurate (redundant) if we said: “Two vectors are equal if they are collinear, codirectional, and have the same length.”

From the point of view of the concept of a free vector, equal vectors are the same vector, as discussed in the previous paragraph.

Vector coordinates on the plane and in space

The first point is to consider vectors on the plane. Let us depict a Cartesian rectangular coordinate system and plot it from the origin of coordinates single vectors and :

Vectors and orthogonal. Orthogonal = Perpendicular. I recommend that you slowly get used to the terms: instead of parallelism and perpendicularity, we use the words respectively collinearity And orthogonality.

Designation: The orthogonality of vectors is written with the usual perpendicularity symbol, for example: .

The vectors under consideration are called coordinate vectors or orts. These vectors form basis on a plane. What a basis is, I think, is intuitively clear to many, more detailed information can be found in the article Linear (non) dependence of vectors. Basis of vectors In simple words, the basis and origin of coordinates define the entire system - this is a kind of foundation on which a full and rich geometric life boils.

Sometimes the constructed basis is called orthonormal basis of the plane: “ortho” - because the coordinate vectors are orthogonal, the adjective “normalized” means unit, i.e. the lengths of the basis vectors are equal to one.

Designation: the basis is usually written in parentheses, inside which in strict sequence basis vectors are listed, for example: . Coordinate vectors it is forbidden rearrange.

Any plane vector the only way expressed as:
, Where - numbers which are called vector coordinates in this basis. And the expression itself called vector decompositionby basis .

Dinner served:

Let's start with the first letter of the alphabet: . The drawing clearly shows that when decomposing a vector into a basis, the ones just discussed are used:
1) the rule for multiplying a vector by a number: and ;
2) addition of vectors according to the triangle rule: .

Now mentally plot the vector from any other point on the plane. It is quite obvious that his decay will “follow him relentlessly.” Here it is, the freedom of the vector - the vector “carries everything with itself.” This property, of course, is true for any vector. It's funny that the basis (free) vectors themselves do not have to be plotted from the origin; one can be drawn, for example, at the bottom left, and the other at the top right, and nothing will change! True, you don’t need to do this, since the teacher will also show originality and draw you a “credit” in an unexpected place.

Vectors illustrate exactly the rule for multiplying a vector by a number, the vector is codirectional with the base vector, the vector is directed opposite to the base vector. For these vectors, one of the coordinates is equal to zero, you can meticulously write it like this:


And the basis vectors, by the way, are like this: (in fact, they are expressed through themselves).

And finally: , . By the way, what is vector subtraction, and why didn’t I talk about the subtraction rule? Somewhere in linear algebra, I don’t remember where, I noted that subtraction is special case addition. Thus, the expansions of the vectors “de” and “e” are easily written as a sum: , . Rearrange the terms and see in the drawing how well the good old addition of vectors according to the triangle rule works in these situations.

The considered decomposition of the form sometimes called vector decomposition in the ort system(i.e. in a system of unit vectors). But this is not the only way to write a vector; the following option is common:

Or with an equal sign:

The basis vectors themselves are written as follows: and

That is, the coordinates of the vector are indicated in parentheses. In practical problems, all three notation options are used.

I doubted whether to speak, but I’ll say it anyway: vector coordinates cannot be rearranged. Strictly in first place we write down the coordinate that corresponds to the unit vector, strictly in second place we write down the coordinate that corresponds to the unit vector. Indeed, and are two different vectors.

We figured out the coordinates on the plane. Now let's look at vectors in three-dimensional space, almost everything is the same here! It will just add one more coordinate. It’s hard to make three-dimensional drawings, so I’ll limit myself to one vector, which for simplicity I’ll set aside from the origin:

Any 3D space vector the only way expand over an orthonormal basis:
, where are the coordinates of the vector (number) in this basis.

Example from the picture: . Let's see how the vector rules work here. First, multiply the vector by the number: (red arrow), (green arrow) and (raspberry arrow). Secondly, here is an example of adding several, in this case three, vectors: . The sum vector begins at the initial point of departure (beginning of the vector) and ends at the final point of arrival (end of the vector).

All vectors of three-dimensional space, naturally, are also free; try to mentally set aside the vector from any other point, and you will understand that its decomposition “will remain with it.”

Similar to the flat case, in addition to writing versions with brackets are widely used: either .

If one (or two) coordinate vectors are missing in the expansion, then zeros are put in their place. Examples:
vector (meticulously ) – let’s write ;
vector (meticulously ) – let’s write ;
vector (meticulously ) – let’s write .

The basis vectors are written as follows:

This, perhaps, is all the minimum theoretical knowledge necessary to solve problems of analytical geometry. There may be a lot of terms and definitions, so I recommend that teapots re-read and comprehend this information again. And it will be useful for any reader to refer to the basic lesson from time to time to better assimilate the material. Collinearity, orthogonality, orthonormal basis, vector decomposition - these and other concepts will be often used in the future. I would like to note that the site materials are not enough to pass a theoretical test or a colloquium in geometry, since I carefully encrypt all theorems (and without proofs) - to the detriment of the scientific style of presentation, but a plus for your understanding of the subject. To receive detailed theoretical information, please bow to Professor Atanasyan.

And we move on to the practical part:

The simplest problems of analytical geometry.
Actions with vectors in coordinates

It is highly advisable to learn how to solve the tasks that will be considered. fully automatic, and the formulas memorize, you don’t even have to remember it on purpose, they will remember it themselves =) This is very important, since other problems of analytical geometry are based on the simplest elementary examples, and it will be annoying to spend additional time eating pawns. There is no need to fasten the top buttons on your shirt; many things are familiar to you from school.

The presentation of the material will follow a parallel course - both for the plane and for space. For the reason that all the formulas... you will see for yourself.

How to find a vector from two points?

If two points of the plane and are given, then the vector has the following coordinates:

If two points in space and are given, then the vector has the following coordinates:

That is, from the coordinates of the end of the vector you need to subtract the corresponding coordinates beginning of the vector.

Exercise: For the same points, write down the formulas for finding the coordinates of the vector. Formulas at the end of the lesson.

Example 1

Given two points of the plane and . Find vector coordinates

Solution: according to the appropriate formula:

Alternatively, the following entry could be used:

Aesthetes will decide this:

Personally, I'm used to the first version of the recording.

Answer:

According to the condition, it was not necessary to construct a drawing (which is typical for problems of analytical geometry), but in order to clarify some points for dummies, I will not be lazy:

You definitely need to understand difference between point coordinates and vector coordinates:

Point coordinates– these are ordinary coordinates in a rectangular coordinate system. I think everyone knows how to plot points on a coordinate plane from the 5th-6th grade. Each point has a strict place on the plane, and they cannot be moved anywhere.

The coordinates of the vector– this is its expansion according to the basis, in this case. Any vector is free, so if necessary, we can easily move it away from some other point in the plane. It is interesting that for vectors you don’t have to build axes or a rectangular coordinate system at all; you only need a basis, in this case an orthonormal basis of the plane.

The records of coordinates of points and coordinates of vectors seem to be similar: , and meaning of coordinates absolutely different, and you should be well aware of this difference. This difference, of course, also applies to space.

Ladies and gentlemen, let's fill our hands:

Example 2

a) Points and are given. Find vectors and .
b) Points are given And . Find vectors and .
c) Points and are given. Find vectors and .
d) Points are given. Find vectors .

Perhaps that's enough. These are examples for you to decide on your own, try not to neglect them, it will pay off ;-). There is no need to make drawings. Solutions and answers at the end of the lesson.

What is important when solving analytical geometry problems? It is important to be EXTREMELY CAREFUL to avoid making the masterful “two plus two equals zero” mistake. I apologize right away if I made a mistake somewhere =)

How to find the length of a segment?

The length, as already noted, is indicated by the modulus sign.

If two points of the plane are given and , then the length of the segment can be calculated using the formula

If two points in space and are given, then the length of the segment can be calculated using the formula

Note: The formulas will remain correct if the corresponding coordinates are swapped: and , but the first option is more standard

Example 3

Solution: according to the appropriate formula:

Answer:

For clarity, I will make a drawing

Segment – this is not a vector, and, of course, you cannot move it anywhere. In addition, if you draw to scale: 1 unit. = 1 cm (two notebook cells), then the resulting answer can be checked with a regular ruler by directly measuring the length of the segment.

Yes, the solution is short, but there are a couple more important points in it that I would like to clarify:

Firstly, in the answer we put the dimension: “units”. The condition does not say WHAT it is, millimeters, centimeters, meters or kilometers. Therefore, a mathematically correct solution would be the general formulation: “units” - abbreviated as “units.”

Secondly, let us repeat the school material, which is useful not only for the task considered:

Please note important technique – removing the multiplier from under the root. As a result of the calculations, we have a result and good mathematical style involves removing the factor from under the root (if possible). In more detail the process looks like this: . Of course, leaving the answer as is would not be a mistake - but it would certainly be a shortcoming and a weighty argument for quibbling on the part of the teacher.

Here are other common cases:

Often the root produces a fairly large number, for example . What to do in such cases? Using the calculator, we check whether the number is divisible by 4: . Yes, it was completely divided, thus: . Or maybe the number can be divided by 4 again? . Thus: . The last digit of the number is odd, so dividing by 4 for the third time will obviously not work. Let's try to divide by nine: . As a result:
Ready.

Conclusion: if under the root we get a number that cannot be extracted as a whole, then we try to remove the factor from under the root - using a calculator we check whether the number is divisible by: 4, 9, 16, 25, 36, 49, etc.

When solving various problems, roots are often encountered; always try to extract factors from under the root in order to avoid a lower grade and unnecessary problems with finalizing your solutions based on the teacher’s comments.

Let's also repeat squaring roots and other powers:

The rules for operating with powers in general form can be found in a school algebra textbook, but I think from the examples given, everything or almost everything is already clear.

Task for independent solution with a segment in space:

Example 4

Points and are given. Find the length of the segment.

The solution and answer are at the end of the lesson.

How to find the length of a vector?

If a plane vector is given, then its length is calculated by the formula.

If a space vector is given, then its length is calculated by the formula .

System-vector psychology- the newest direction in psychology, formed twelve years ago. The founder is a psychoanalyst Yuri Burlan, which currently systematically conducts its seminars, courses, and trainings. It’s interesting that they also take place online on the Internet, attracting thousands of viewers and listeners.

Yu. Burlan himself says that he main task- to make a person happy, to make sure that after his training, clients leave with the main skill - the ability to enjoy life and smile, everything else, according to the psychologist, will work out on its own.

Since the main emphasis in this direction is on unconscious, and the personality typology is based on erogenous zones person, he can be described as branch of psychoanalysis. Although sometimes system-vector psychology is defined not just as a separate direction in psychology, but as a new broad field of knowledge, a complex science about man.

System-vector psychology and systemic psychoanalysis is an extensive system of psychological knowledge about a person, a direction in applied psychology.

Yu. Burlan touches on sociology, pedagogy and even politics, explaining his theory; he takes a comprehensive approach to understanding the phenomenon of personality functioning in society.

Species role and vector

In system-vector psychology, a person is considered as an integral complex system in a social system, and this system is not only physical and mental, but also social. Burlan assigns a special role in the formation of personality society and the instinct of procreation.

Human, according to Yu. Burlan, this is a clot of a living being that wants to have fun, enjoy. This desire and desire for pleasure in the body is expressed through the erogenous zones.

Society pushes for development not only of a specific person, but also of humanity as a species. When in ancient times people began to gather together and live in groups in order to survive, humans developed special characteristics and desires. Today we say that they were based on two basic unconscious needs, initially, apparently, these were not needs, but group tasks of primitive people. And these needs-tasks:

• saving life,
• procreation.

Since human development is a movement in a certain direction, it must have a vector, a guideline. The main thing becomes the vector wish personality. Desire gives rise to thought, thought forms intention, and intention pushes to action, which shapes the role of a person in society, species role.

In the primitive pack, each person had his own specific species role, duty, work that he performed for the common good.

A person cannot live alone; he has long united and continues to exist in a single system of relations between people called society. From birth, nature endows a person with everything necessary (intelligence, abilities, feelings, temperament, and so on) so that he can become happy, fulfill all his desires and fulfill his species role.

Along with the development of society, man also developed. The more complex the society, the more multifaceted the mental structure of the individual becomes. Already
So many generations of people have changed that desires, needs, behavior, and human relationships have become so complicated that behind them it is difficult to discern those first, primitive, but already conscious actions in the community, the species role.

Meanwhile, this role is unconscious level still continues determine personality characteristics and its social orientation.

Modern man, not realizing his role in society (by and large, his purpose), is moving in the wrong direction or even in reverse side from happiness.

The role is determined by the desire to enjoy life. Depending on which erogenous zone is predominant for the expression of this desire, eight personality types.

Types of personality orientation

The type of thinking, values, priorities of a person, his sexuality, mental state, physical health and degree of satisfaction with life depend on the vector.

The vector qualities given by nature cannot be changed, but it is necessary develop and implement them your inner potential. Innate properties and qualities develop from the birth of a person to his full puberty.

Brief description of the eight vectors, defining the inner world of a person at an unconscious level:

1. Cutaneous. Species role in primitive society - hunter and guard of the territory, functions: prohibitive, restrictive.

Suitable professions: athlete, engineer, inventor, military man, businessman.

Personal qualities: responsibility, rationality, discipline, activity, competitiveness, punctuality, ambition, economy. Logical thinking prevails, they are not afraid of change, they strive for leadership, success, wealth, social status, and want to achieve heights in their career. They are well oriented in time and space.

Approximately 24% of the population belongs to this type.

1. Anal. Species role – keeper of the cave, hearth, “rear”; functions: transfer of accumulated experience to next generations.

Suitable professions: teacher, doctor, housewife/family man.

Personal qualities: stubborn and principled, but easily wounded, strong-willed, diligent, dutiful, reliable, honest, loyal, indecisive, vindictive, conservative. These are intellectuals prone to perfectionism, they strive to do everything perfectly, so they can be high professionals in any field. Analytical thinking predominates. Such people have excellent memory.

Approximately 20% of the population belongs to this type.

1. Muscular. Species role: warrior and hunter, function: protective.

Suitable professions: factory worker, construction worker, agricultural worker and other representative of the working class, as well as the military.

Personal qualities: hard work, diligence, unpretentiousness, endurance, simplicity (basic needs: food, sleep, sex), peacefulness. Thinking is rigid, visually effective, the mind is activated only in the process of muscle work.

Approximately 38% of the population belongs to this type.

1. Urethral. Species role – leader, functions: responsibility for survival, management, expansion of the flock and its habitat.

Suitable professions: all related to leadership and management of people, up to the president of the country.

Personal qualities: innate altruism, optimism, activity, initiative, fearlessness, fair, mercy, cunning, unpredictability. Thinking is tactical and creative.

Suitable professions: psychologist, doctor, teacher, educator, designer, film director and other artists and cultural figures.

Personal qualities: kindness, responsiveness, understanding, empathy, amorousness, modesty, conscientiousness, suggestibility, daydreaming, coquetry, emotionality. Such people are dreamers, they think in images.

Approximately 5% of the population belongs to this type.

1. Sound. Species role – night guard of the flock, functions: protection at night, feedback to the root cause.

Suitable professions: philosopher, composer, programmer, translator, writer, poet.

Personal qualities: idealists (and their desires are mainly intangible), reasonable, focused, self-absorbed, self-centered, unemotional, aloof. Abstract thinking.

Approximately 5% of the population belongs to this type.

1. Oral. Species role – beater of prey, herald, jester; functions: warning of danger, call for unity.

Suitable professions: cook, singer, commentator, speaker.

Personal qualities: cheerfulness, sociability, humor, charm, sense of humor. Such people tend to lie and mock. They think when they speak, that is, their thinking is verbal.

Approximately 5% of the population belongs to this type.

1. Olfactory. Specific role – intelligence officer, adviser to the leader, sorcerer, “gray eminence”; functions: strategic intelligence.

Suitable professions: intelligence officer, politician, financier.

Personality traits: melancholic, calm, intuitive, impartial, sometimes immoral and insidious. Such individuals think intuitively, on an unconscious level.

Approximately 1% of the population belongs to this type.

Why do you need to know your vector?

In the primitive pack, each person had one, specific vector, since this society was primitive. Today, the type of personality orientation usually consists of several vectors, on average from 3-4 -X. People whose orientation consists of seven or even all eight vectors, as a rule, are outstanding or brilliant.

The presence of several vectors at once means that modern man There is more possibilities for self-realization and chances for happiness. But this is how the world and people work, that often what should be a source of pleasure turns into a reason for suffering. Due to the ignorance and unwillingness of many people to understand themselves, the system called “man” fails.

Although the author of the concept emphasizes that pure types are very, very rare, by identifying your dominant vector type, you can learn a lot about yourself, understand problems and find ways to solve them. The vector of personality is always aimed at self-realization and achieving well-being.

A nice bonus: if you learn to distinguish personality types by vector, the process of understanding and communicating with people around you will become easier and improve.

The description of the eight vectors is the basis of the principles of system-vector psychology and at the same time basic idea. If you “dig” this direction deeper, you will find that Yu. Burlan touches on and explains many phenomena of the inner world of man and the external world of society.

Systemic psychoanalysis is becoming fashionable in Russia and throughout the post-Soviet space. It is already effectively used not only in psychology, but also in medicine and pedagogy. People are attracted to this direction by the special, systemic thinking and worldview to which Yu. Burlan “switches” a person. His approach is unusual and controversial, but nevertheless popular.

The section is very easy to use. Just enter the desired word in the field provided, and we will give you a list of its meanings. I would like to note that our site provides data from various sources - encyclopedic, explanatory, word-formation dictionaries. Here you can also see examples of the use of the word you entered.

Meaning of the word vector

vector in the crossword dictionary

Dictionary of medical terms

Explanatory dictionary of the Russian language. S.I.Ozhegov, N.Yu.Shvedova.

vector

A, m. (special). A mathematical quantity represented by a straight line segment, characterized by its numerical value and direction.

adj. vector, -aya, -oe. Vector calculus (mathematical discipline).

New explanatory and word-formative dictionary of the Russian language, T. F. Efremova.

vector

m. A straight segment characterized by a numerical value and a certain direction.

Encyclopedic Dictionary, 1998

vector

VECTOR (from Latin vector - carrier) a segment of a certain length and direction. Usually a vector is denoted by the letter a or (the first letter is the beginning, the second is the end of the segment); the absolute value (length) of the vector is written |a| or. Two vectors are equal only if they have the same lengths and the same directions (that is, they are parallel and equally oriented). With a change in orientation, the sign of the vector changes. Vectors depict the so-called. vector quantities: force, speed, acceleration, etc. Actions on a vector are studied in vector calculus.

vector

VECTOR in molecular genetics is a self-replicating DNA molecule capable of incorporating foreign DNA (genes) and transferring it into cells whose hereditary properties are desired to be changed. Typically, a vector is created based on the DNA of plasmids and viruses (including bacteriophages). The vector is widely used in genetic engineering for propagation (cloning) of introduced genes or for obtaining protein products encoded by these genes.

Vector

(from Latin vector, literally ≈ carrying, transporting), in a geometric sense ≈ a directed segment, that is, a segment that has a beginning (also called the V. application point) and an end. To designate V., either bold Latin letters a are used , b , or letters of the regular alphabet with dashes or arrows at the top:

V., having a beginning at point A and an end at point B, is designated. The straight line on which the V. is located is called the line of action of this V.

The concept of velocity arose in connection with the study of quantities characterized by numerical value and direction (for example, the displacement, speed, and acceleration of a moving material point, the force acting on it, etc.). In mechanics and physics, free, sliding and bound vectors are considered. A vector is called free if its value does not change with arbitrary parallel translation. Free velocity is, for example, the speed of movement of a material point. A wave is called sliding if its value does not change with any parallel translation along the line of its action. An example of a sliding force is a force acting on an absolutely rigid body (two equal forces located on the same straight line have the same effect on an absolutely rigid body). A wave is called connected if its beginning is fixed. For example, a force applied to a certain point of an elastic body represents a bound wave. The properties of free waves are studied by means of vector algebra (see Vector calculus). General concept V. as an element of the so-called vector space is defined axiomatically.

Lit.: Ilyin V. A., Poznyak E. G., Analytical geometry, M., 1968.

E. G. Poznyak.

Wikipedia

Vector

Vector .

Vector (mathematics)

Vector- in the simplest case, a mathematical object characterized by magnitude and direction. For example, in geometry and the natural sciences, a vector is a directed line segment in Euclidean space.

Examples: radius vector, speed, moment of force. If a coordinate system is given in space, then the vector is uniquely defined by a set of its coordinates. Therefore, in mathematics, computer science and other sciences, an ordered set of numbers is often also called a vector. In a more general sense, a vector in mathematics is considered as an element of some vector space.

It is one of the fundamental concepts of linear algebra. When using the most general definition, almost all objects studied in linear algebra, including matrices and tensors, are vectors; however, if these objects are present in the surrounding context, a vector is understood, respectively, as a row vector or a column vector, a tensor of the first rank. The properties of operations on vectors are studied in vector calculus.

Vector (geometry)

vector- a directed line segment, that is, a segment for which it is indicated which of its boundary points is the beginning and which is the end.

Vector starting at a point A and end at a point B usually denoted as $\overrightarrow(AB)$. Vectors can also be denoted in small letters with an arrow above them, for example a⃗. Another common way of writing is to highlight the vector symbol in bold: a.

A vector in geometry is naturally associated with translation (parallel translation), which obviously clarifies the origin of its name (, carrier). Indeed, each directed segment uniquely defines some parallel translation of the plane or space: say, the vector $\overrightarrow(AB)$ naturally determines the translation at which the point A will go to point B, also vice versa, parallel transfer, in which A goes into B, defines a single directed segment $\overrightarrow(AB)$ (the only one - if we consider all directed segments of the same direction and length to be equal - that is, consider them as free vectors; indeed, with parallel translation, all points are shifted in the same direction by the same distance, so in this understanding $\overrightarrow(A_1B_1) = \overrightarrow(A_2B_2) = \overrightarrow(A_3B_3) =\dots$).

The interpretation of a vector as a transfer allows us to introduce the operation of adding vectors in a natural and intuitively obvious way - as a composition of transfers; the same applies to the operation of multiplying a vector by a number.

Vector (molecular biology)

Vector (in genetics) is a nucleic acid molecule, most often DNA, used in genetic engineering to transfer genetic material to another cell.

Existing vectors:

• phasmids
• vectors based on the SV40 virus
• adenovirus-based vectors
• vectors based on herpes viruses
• retrovirus-based vectors
• adeno-associated virus vectors

Vector (factory)

JSC "Ural Production Enterprise "Vector""- a military enterprise specializing in the production of communications equipment, consumer goods and industrial and technical purposes. Located in Yekaterinburg. It is part of the Almaz-Antey air defense concern.

Organized in 1941 on the basis of the Moscow Geodesy plant evacuated to Sverdlovsk.

At first it was called Plant No. 356, in 1966-1992 - Sverdlovsk Electrical Automatics Plant.

In 2002, the federal state unitary enterprise "Vector" by Decree of the President of the Russian Federation and the decision of the Ministry for State Property Management Sverdlovsk region was transformed into OJSC Ural Production Enterprise Vector, 100% of the shares of which remained in state ownership.

“Vector” for 15 years was a monopolist in the production of domestic electric musical instruments and sound amplification equipment. 1.

The enterprise was awarded the Order of the Red Banner of Labor in 1966 for the success achieved in fulfilling the tasks of the seven-year plan.

Vector (research center)

SSC VB "Vector"- one of the largest scientific virological and biotechnological centers in Russia, located in the science city of Koltsovo, Novosibirsk region, a few kilometers from Novosibirsk. The city-forming enterprise around which the current Science City r.p. appeared. Koltsovo.

The full name of the center is Federal budgetary institution science “State Scientific Center for Virology and Biotechnology “Vector”” of the Federal Service for Surveillance in the Sphere of Consumer Rights Protection and Human Welfare.

The mission of the Center is declared to be “ scientific and practical support for countering global infectious threats" At the State Scientific Center for Virology and Biochemistry "Vector" fundamental research work is carried out in the field of epidemiology, molecular biology, virology, bacteriology, genetic engineering, biotechnology, ecology and biological safety.

The Center includes a branch - the Institute of Medical Biotechnology, located in Berdsk.

Examples of the use of the word vector in literature.

All nations have a biological sense of the fullness of the area, manifested in each individual of the nation, and therefore we can talk about the biological sex of the nation, and therefore about vector of this field - respectively in each individual.

That is, I admit, of course, the likelihood of a change vector Sibur is in love, but this, unfortunately, will not happen next time.

But - only on the condition that the glide path is in the center, which means that the plane is moving along the hypotenuse, and all the laws of addition vectors act.

What vector function of a prime number will be an individualizing function of the field of complex numbers, the values ​​of which will be invariant forms, invariants, referents, products, divisions, exponentiations of complex numbers, quarterions, the logic of which is the invariance of the same actions over complex numbers, as the very possibility of actions with complex numbers, a modality whose object is a quantum, the concept of which is the condition for the flux of quarterions to be equal to zero.

In the past, nutmeg was given to hysterical women, and tests surprisingly confirmed vector the actions of this remedy.

You see, according to my calculations, the position of this thread in space at each moment of time is vector, collinear to the tangent to the curve of movement of my center of mass along the corridor of department 1B.

Am I freely falling or am I forcibly ascending to the heights - where I am actually directed vector my converting activity?

Libby's brain almost automatically began to work on the incredibly complex problem of the relationship between accelerations, intervals, vectors movements.

So, having determined geographical coordinates studied breed and direction vector magnetization, you can find out where the Earth's magnetic pole was at the time when the rock solidified.

Field Headquarters of the Third Guards, Prince Davion, Regiment Dunkeld Glengarry Spaceport, Route vector Skye Federated Commonwealth Estimated time 1314 May 13, 3057 Inside the large walking all-terrain vehicle, where the field headquarters of the Third Guards Regiment was located, it was, as always, gloomy and quiet, except for the chirping of communication devices, the beeping and hum of electronic devices, the faint glow of monitors, call signals and yes quiet voices coming from the speakers served as a kind of background, against which the roar of a close battle could be heard especially clearly.

In front of Janelle's eyes, a rocket was drawn vector, indicating the aiming point, took the direction exactly towards the enemy ship.

And some enlightened academician or artist vector acquisitiveness in life's prudence is directed just the opposite - back, into the familiar crimson darkness of this half-century.

What provides lifting force and transfer energy, after all, it doesn’t go with the wind, it’s no secret that vector blowing off, as far as one can judge from the belatedly included statistics, has never been oriented inward to the country, and therefore some ideologists have already broadcast with visible evidence that the Slavs have finally generated some kind of special compression purifying biofield, pushing all the pampered, thin-skinned and nervous ones to the margins of the world half-breeds.

As you understand, I mean a scalar value of speed, since when running in a circle vector constantly changing.

Then you should put the address of the first byte of data in vector interruptions.