Among all unit vectors $\vec{u}= \left\lbrack\begin{array}{c} x \\ y \\ z\end{array} \right\rbrack$ in ${\mathbb R}^3$, find the one for which the sum $x + 3 y + 6 z$ is minimal.

$\vec{u}=$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$