Unit vector

1

"Divide the position vector by its magnitude"

Example

$$\overrightarrow {AB} = - 4i + 12j + 3k$$

Magnitude:

$$\left| {\overrightarrow {AB} } \right| = \sqrt {{{\left( { - 4} \right)}^2} + {{\left( {12} \right)}^2} + {{\left( 3 \right)}^2}} = 13$$

Unit vector:

$$\overrightarrow u = {{\overrightarrow {AB} } \over {\left| {\overrightarrow {AB} } \right|}} = {{ - 4i + 12j + 3k} \over {13}} = - {4 \over {13}}i + {{12} \over {13}}j + {3 \over {13}}k$$