# 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..

Turn on the subtitles if needed