#### 1. NOTION OF VECTOR

A segment* A*B with a starting poi

*t A and an end poi*

**n***t B is ca*

**n****lled a directed segm**ent

**or vecto**r (Fig. 1). The vecto

*AV is denoted*

**r***B.*

**A**A vector that coincides with the start and end point is called t**he zero vecto**r and is denoted by 0.

The length of the vector * AB *is denoted by | A

*d is called t*

**B | an****he mod**ul

**us (intensit**y) of the vector.

Fig. 1

The line on which the vector lies determines its direction. Vectors lying on the same line or parallel lines have the same direction. They are said to be** collinear vectors.**

A vector whose length is a unit is calle**d a unit vector** or o**rth**.

For two vectors AB* an*d CD

*e say that they are equal if they have the same length, the same direction and the same direction.*

**w**Two collinear vectors of equal length and opposite directions are calle**d opposite vectors.**

**2. COLLECTION OF VECTORS**

For any three points O,* *A a

*d B*

**n***in a plane the equation applies*

**OB = OA + AB**

which is ca**lled a three-point rule.** The vectors* O*A a

*AB are call*

**nd****ed contiguous vectors.**

The sum of two (or finite) conjoined vectors is a vector whose beginning is at the beginning of the first and end at the end of the second (last) vector (fig. 2).

Fig. 2

**Collection properties**

1. *a + o = a*

2. **a + (- a) = 0**

3. **a + b = b + a**

*(commutative property)*

4. **(a + b) + c = a + (b + c)**

*(associative property)*

#### 3. **SUBTRACTION OF VECTORS**

The difference of the vect* or*s a

*and b is the v*

*ctor x, for which the equation is fulfilled*

**e*** b – x = a* (Fig. Z)

Fig.3

Subtraction properties:

#### 4. **MULTIPLICATION OF VECTOR WITH NUMBER**

The product ka = ak of the vector a and the n* umber* k ∈ R is a

*vector b of*

*| ∙ | a |*

**length | k***f*

**, whic**h*≠ 0 and a ≠ 0 is equ*

**or k***distan*

**i***a, if k> 0, and opposite*

**t with***o a, i*

**t***o.*

**f k <**Properties of vector multiplication by number: