Answer
$$\left\langle\frac{2}{3},-\frac{2}{3},-\frac{1}{3}, \right\rangle.$$
Work Step by Step
The unit vector in the direction opposite to $ v=\langle -4,4,2 \rangle $ is $-e_v $ and is given by
$$-e_v=-\frac{v}{\|v\|}=-\frac{\langle -4,4,2 \rangle }{\sqrt{16+16+4}}\\
=-\left\langle-\frac{4}{6},\frac{4}{6},\frac{2}{6}, \right\rangle=\left\langle\frac{4}{6},-\frac{4}{6},-\frac{2}{6}, \right\rangle\\
=\left\langle\frac{2}{3},-\frac{2}{3},-\frac{1}{3}, \right\rangle.$$
