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
$||v||=\sqrt{(-6)^2+12^2+4^2}\\||v||=\sqrt{36+144+16}\\||v||=\sqrt{196}\\||v||=14.$
Thus the unit vector is: $u=\frac{-6i+12j+4k}{14}=\\u=-\frac{3}{7}i+\frac{6}{7}j+\frac{2}{7}k.$
