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:

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