Mathematics

Problem

\vec{u} = 2\hat{i} + 2\hat{j} - \hat{k}

and

\vec{v} = 6\hat{i} - 3\hat{j} + 2\hat{k}

, then a unit vector perpendicular to both

\vec{u}

and

\vec{v}

is (A)

\hat{i} - 10\hat{j} - 18\hat{k}

(B)

\frac{1}{\sqrt{17}} \left( \frac{1}{5}\hat{i} - 2\hat{j} - \frac{18}{5}\hat{k} \right)

(C)

\frac{1}{\sqrt{473}} (7\hat{i} - 10\hat{j} - 18\hat{k})

(D)

\frac{1}{\sqrt{425}} (\hat{i} - 10\hat{j} - 18\hat{k})