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.