Find a basis of the subspace of ${\mathbb R}^4$ that consists of all vectors perpendicular to both $$\left[\begin{array}{c} 1\cr 0\cr -6\cr 1 \end{array}\right] \ \ \ \ \mbox{and} \ \ \ \ \left[\begin{array}{c} 0\cr 1\cr -6\cr 5 \end{array}\right].$$
Basis: $\Bigg\lbrace$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$, $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$ $\Bigg\rbrace.$