What is the unit vector perpendicular to t

$\vec A = 2\hat i + 2\hat j - \hat k$ and $\vec B = 6\hat i - 3\hat j + 2\hat k$

$\vec C = \vec A \times \vec B = \left( {2\hat i +2\hat j - \hat k} \right) \times \left( {6\hat i - 3\hat j + 2\hat k}\right)$

$ = \left| {\,\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\2&2&{ - 1}\\6&{ - 3}&2\end{array}\,} \right|$$ = \hat i - 10\hat j - 18\hat k$

Unit vector perpendicular to both $\vec A$ and $\vec B$

$ = \frac{{\hat i - 10\hat j - 18\hat k}}{{\sqrt {{1^2} + {{10}^2} + {{18}^2}} \,}}$

$ = \frac{{\hat i - 10\hat j - 18\hat k}}{{5\sqrt {17} }}$