# Vectors

A vector describes a movement from one point to another. A vector quantity has both and (size).

A quantity has only magnitude.

A vector can be represented by a line segment labelled with an arrow.

A vector between two points A and B is described as: , or .

The vector can also be represented by the column vector . The top number is how many to move in the positive -direction and the bottom number is how many to move in the positive -direction.

Vectors are equal if they have the same magnitude and direction regardless of where they are.

So

A negative vector has the same magnitude but the opposite direction.

Vector is the same as travelling backwards down the vector .

### Example

Write, in terms of , and , the vectors , , and .

and are equal vectors, they have the same magnitude and direction.

and are equal vectors, they have the same magnitude and direction.

has the same magnitude as but the opposite direction.

has the same magnitude as but the opposite direction.