**Vectors**

A vector has direction and length. In physics, vectors describe physical quantities with a certain direction and magnitude, such as forces. A vector is drawn as an arrow. A vector has no origin i.e. vectors in the same direction and lengths are the same vector.

A vector is usually named with a letter and a line is drawn above the letter to indicate that it is a vector. There is a vector *a* in this figure. Sometimes, you can use an arrow instead of a line above the letter. The length of the vector is denoted by an absolute value. A unit vector is a vector with a length of 1.

Notation

A vector can also be named with a start and end point. Here is a vector which starts at point* A* and ends at point *B*. It's read as vector* A to B* or vector *AB*.

If vectors are parallel and of equal length, it is the same vector. The figure shows vectors *a* and *b*, both of which have a length of *3*. The vectors are parallel, so it is the same vector.

### Multiplying a vector by a number

A vector twice in a row, forms a vector with a length that is twice the original and parallel to it. In the figure, after vector* a* with length *3*, vector *a* is set again. Vector* 2a *with a length of* 6* is obtained.

Multiplying a vector by a positive number only changes its length, not its direction. When multiplied by a negative number, the direction of the vector changes to the opposite direction.

### Addition of vectors

In the addition of vectors, the vectors are placed in sequence. The sum vector is a vector from the beginning of the first vector to the end of the last vector.

Denote the side edges of a rectangular parallelogram with vectors *a, b,* and* c.*

We can describe the diagonal vectors *BG* and* BF* with the edge vectors..

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