Let $L$ be the line given by the span of $\left[\begin{array}{c} -6\cr 1\cr -6 \end{array}\right]$ in $\mathbb{R}^3$. Find a basis for the orthogonal complement $L^{\bot}$ of $L$.

A basis for $L^{\bot}$ is $\Bigg\lbrace$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$, $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$ $\Bigg\rbrace.$