I don't see why the inclusion of "t" should throw you off. For any vector $\displaystyle \begin{align*} \mathbf{a} \end{align*}$, its unit vector parallel to $\displaystyle \begin{align*} \mathbf{a} \end{align*}$ is $\displaystyle \begin{align*} \hat{\mathbf{a}} = \frac{\mathbf{a}}{ \left| \mathbf{a} \right| } \end{align*}$. It doesn't matter if this vector happens to be a function of another variable...