Unit Vector

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

vector magnitude and direction

Unit Vector

A Unit Vector has a magnitude of 1:

unit vector


The symbol is usually a lowercase
letter with a "hat", such as:
vector a-hat
(Pronounced "a-hat")


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:

vector unit scale 1 to 2.5

In 2 Dimensions

Unit vectors can be used in 2 dimensions:

vector a = 2x + 1.3y

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:

vector unit 3d

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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