Answer
$\vec{u}=\begin{bmatrix}
-6/\sqrt{61}\\
4/\sqrt{61}\\
-3/\sqrt{61}
\end{bmatrix}$
Work Step by Step
$\vec{v}=\begin{bmatrix}
-6\\
4\\
-3
\end{bmatrix}$
$||\vec{v}||=\sqrt{\vec{v}\cdot\vec{v}}=\sqrt{(-6)^2+4^2+(-3)^2}=\sqrt{61}$
$\vec{u}=\frac{\vec{v}}{||\vec{v}||}=\begin{bmatrix}
-6/\sqrt{61}\\
4/\sqrt{61}\\
-3/\sqrt{61}
\end{bmatrix}$