Answer
$\frac{3}{7}i-\frac{6}{7}j-\frac{2}{7}k.$
Work Step by Step
If $v=ai+bj+ck$ and $||v||=\sqrt{a^2+b^2+c^2}$, then the unit vector $u$ in the same direction as $v$ is
$u=\frac{v}{||v||}$.
The magnitude of $v$ is
$||v||=\sqrt{3^2+(-6)^2+(-2)^2}\\||v||=\sqrt{9+36+4}\\||v||=\sqrt{49}=7.$
Thus the unit vector is: $u=\frac{3i-6j-2k}{7}\\u=\frac{3}{7}i-\frac{6}{7}j-\frac{2}{7}k.$
