Find the cross product a=2i+3j+k & …

{tex}\eqalign{ & {\rm{Here,}}\vec a = 2\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over i} + 3\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over j} + \hat k \cr & {\rm{ }}\vec b = \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over i} - \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over j} + 2\hat k \cr & {\rm{ \vec a \times \vec b = }}\left| {\matrix{ {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over i} } & {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over j} } & {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over k} } \cr 2 & 3 & 1 \cr 1 & { - 1} & 2 \cr } } \right| \cr & = \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over i} \left[ {3 \times 2 - 1 \times ( - 1)} \right] - \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over j} \left[ {2 \times 2 - 1 \times (1)} \right] + \hat k\left[ {2 \times ( - 1) - 3 \times 1} \right] \cr & = 7\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over i} - 3\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over j} - 5\hat k \cr} {/tex}