## Unit Vectors

## Definition: A unit vector is a vector of length 1

i.e. |U| = 1. (|U| is its length.)

Suppose a = (x

_{a}, y_{a}) and b = (x_{b}, y_{b}). The vector shown here is set up so that (x_{b}- x_{a})^{2}+ (y_{b}- y_{a})^{2}= 1, i.e. U has length one.In the sketch, you can check it out by moving a to your favorite points and then see what you can choose for b; when you find a nice vector you can add its coordinates to the table by double-clicking on it.