Unit Vector - Math Is Fun

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Math is Fun Advanced 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")

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:

vector unit scale 1 to 2.5

In 2 Dimensions

Unit vectors can be used in 2 dimensions:

vector a em=/em 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. 3044, 3045, 3046, 3047, 3048, 3049, 3909, 3910, 3911, 3912 Vectors Algebra Index Copyright © 2025 Rod Pierce

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