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
You can use unit vectors to help you work with vectors 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:
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