Answer
$$ \left\langle\frac{1}{5\sqrt{2}},0,\frac{7}{5\sqrt{2}} \right\rangle.$$
Work Step by Step
The unit vector in the direction of $ u=\langle 1,0,7 \rangle $ is $ e_u $ and is given by
$$ e_u=\frac{u}{\|u\|}=\frac{\langle 1,0,7 \rangle }{\sqrt{1^{2}+0^{2}+7^{2}}}\\
=\left\langle\frac{1}{5\sqrt{2}},0,\frac{7}{5\sqrt{2}} \right\rangle$$
