Answer
$\dfrac{\overrightarrow{v}}{|v|},-\dfrac{\overrightarrow{v}}{|v|}$
Work Step by Step
We consider the unit vector $\dfrac{\overrightarrow{v}}{|v|}$, which is parallel to $\overrightarrow{v}$.
Another unit vector also parallel to $\overrightarrow{v}$ is $-\dfrac{\overrightarrow{v}}{|v|}$.