$\overrightarrow A \, \times \,\overrightarrow B \,$

$ = \left| {\,\begin{array}{*{20}{c}}{\hat i\,\,}&{\hat j\,\,}&{\hat k}\\{3\,\,}&{1\,\,}&2\\{2\,\,\,}&{ – 2\,\,\,}&4\end{array}\,} \right|\,  $

$=(1 \times 4 – 2 \times – 2)\hat i + (2 \times 2 – 4 \times 3)\hat j + (3 \times – 2 – 1 \times 2)\hat k$ $ = 8\hat i – 8\hat j – 8\hat k$

$\overrightarrow {\rm{A}} \, \times \overrightarrow {\rm{B}} \, = \,|\overrightarrow {\rm{A}} \times \overrightarrow {\rm{B}} |\, = \sqrt {{{(8)}^2} + {{( – 8)}^2} + {{( – 8)}^2}} \,$ $ = 8\sqrt 3 $