Definition:Unit Vector

Definition
Let $\mathbf v$ be a vector quantity.

The unit vector in the direction of $\mathbf v$ is defined and denoted as:
 * $\hat {\mathbf v} = \dfrac {\mathbf v} {\left\lvert{\mathbf v}\right\rvert}$

where $\left\lvert{\mathbf v}\right\rvert$ is the magnitude of $\mathbf v$.

Also presented as
The unit vector can often be seen as:
 * $\hat {\mathbf v} = \dfrac {\mathbf v} v$

as in this context $v$ is usually understood as being the magnitude of $\mathbf v$.