Explanation

(c) Let $\overrightarrow{C}$ be a vector perpendicular to $\overrightarrow{A}\ $ and $\overrightarrow{B}$
Then as per question $k\overrightarrow{C} = \overrightarrow{A}\ \times \overrightarrow{B}$
or $k = \frac{(\overrightarrow{A}\ \times \overrightarrow{B})}{\overrightarrow{C}}$
$= \frac{\left( 2\widehat{i} + 3\widehat{j} + 6\widehat{k} \right) \times (3\widehat{i} - 6\widehat{j} + 2\widehat{k})}{(6\widehat{k} + 2\widehat{j} - 3\widehat{k})}$
$= \frac{(42\widehat{i} + 14\widehat{j} - 21\widehat{k})}{(6\widehat{i} + 2\widehat{j} - 3\widehat{k})} = 7$