Answer
$\langle \frac{-2}{3},\frac{1}{3}, \frac{2}{3}\rangle$
Work Step by Step
Let $\mathbf v=\langle -4,2,4 \rangle$. We can obtain a unit vector in the same direction as $\mathbf v$ by multiplying $\mathbf v$ by $\frac{1}{|\mathbf v|}$.
By definition, $|\mathbf v|=\sqrt{(-4)^2+2^2+4^2}=\sqrt{16+4+16}=\sqrt{36}=6$.
So $\frac{\mathbf v}{|\mathbf v|}=\frac{\mathbf v}{6}=\frac{\langle -4,2,4 \rangle}{6}=\langle \frac{-4}{6},\frac{2}{6}, \frac{4}{6}\rangle =\langle \frac{-2}{3},\frac{1}{3}, \frac{2}{3}\rangle$ is a unit vector in the same direction as $\mathbf v$.
