# Unit Vector

A vector has **magnitude** (how long it is) and **direction**:

## Unit Vector

A **Unit Vector** has a magnitude of **1**:

The symbol is usually a lowercase letter with a "hat", such as: |

(Pronounced "a-hat") |

## Scaling

A vector can be "scaled" off the unit vector. Here vector **a** is shown to be 2.5 times a unit vector. Notice they still point in the same direction:

## In 2 Dimensions

Unit vectors can be used in 2 dimensions:

Here we show that the vector **a** is made up of 2 "x" unit vectors and 1.3 "y" unit vectors.

## In 3 Dimensions

Likewise we can use unit vectors in three (or more!) dimensions:

Advanced topic: arranged like this the three unit vectors form a **basis** of 3D space. But that is not the only way to do this! Learn more at Matrix Rank.

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