c
(c) \(\vec A = 2\hat i + 2\hat j - \hat k\) 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 \(\vec B\) \( = \frac{{\hat i - 10\hat j - 18\hat k}}{{\sqrt {{1^2} + {{10}^2} + {{18}^2}} \,}}\)

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