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Астана

00:00:01

concept of a vector, many physical

00:00:03

quantities, in addition to their numerical

00:00:05

value, are also characterized by

00:00:06

direction, for example force or speed,

00:00:08

such quantities are called vector

00:00:10

quantities

00:00:11

or vectors for short in this lesson we

00:00:13

will understand what a vector is from the point of

00:00:14

view of mathematics night we have

00:00:16

some a segment,

00:00:17

both points a and b are called the ends of this

00:00:23

segment or boundary points,

00:00:25

so a segment for which it is indicated

00:00:27

which of its boundary points is the

00:00:30

beginning and which is the end

00:00:32

is called a directed segment or

00:00:34

vectors are usually designated as if we have a

00:00:37

this is the beginning b the end then we put

00:00:40

an arrow here and they say that a.b.

00:00:42

this vector is worth such an arrow sign

00:00:45

this is to begin Victor in this way and you

00:00:47

now have a direction if we

00:00:50

write a vector a b then we mean that

00:00:52

point a is the beginning. b the end if it is

00:00:55

clear from the context which point

00:00:57

is the beginning which to the father we can

00:00:59

denote this vector with one small

00:01:01

letter and put a vector sign above it

00:01:05

then we say electro

00:01:07

for example in a triangle a b c we can

00:01:12

mark the next vector a and vector b

00:01:16

vector bc vector c a

00:01:19

but also we can mark vector b and

00:01:21

vector a and vector c in this

00:01:26

triangle we have established 6 different

00:01:28

vectors, we also introduce the concept of 0

00:01:30

vector, zero vector is a vector

00:01:33

whose beginning coincides with the end, it’s

00:01:35

not difficult to guess, in fact it’s

00:01:37

simple. on the plane

00:01:38

if we have some . m then it

00:01:42

can also be considered as a vector means

00:01:43

vector m m t m is the beginning and

00:01:47

the end, sometimes it is convenient to use the

00:01:49

following notation by putting 0 and putting a

00:01:52

sign on the vector, it turns out this is a zero

00:01:55

vector,

00:01:56

that is, a zero vector is any point

00:01:58

on the plane, also a vector

00:02:00

is characterized by its length the length of the

00:02:02

vector b is the length of the

00:02:04

corresponding segment, that is, when

00:02:07

we talk about the length of the vector b

00:02:10

denotes the

00:02:11

signs of the modulus, then we mean the length of

00:02:13

the segment a.b.

00:02:16

let's look at an example, let's say we

00:02:19

have a square with side 2 abcd

00:02:26

is required for the length of the vector a c

00:02:29

let's first draw this vector

00:02:31

if we have a vector a of the center is the

00:02:33

beginning c is the end that is, from a the

00:02:36

arrow kc

00:02:38

we need to find the length of the vector a c that's what we

00:02:42

said that the length of the vector is the length of the

00:02:44

corresponding segment then we need to

00:02:46

find just the length of the segment tion but it is

00:02:48

found easily so this square bc

00:02:51

we also have two losses of Pythagoras is the

00:02:54

father this will be two roots of 2

00:02:55

so the length of the vector c will be two

00:02:58

roots sound let’s also note the fact that the

00:03:00

length of the 0 vector is equal to zero, that is,

00:03:03

if we are talking about the length of the 0 vector, that we

00:03:06

say that it is equal to zero, this is the

00:03:09

end of this breeze

00:03:10

[music]

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