Answer
\[{\mathbf{u}} \times {\mathbf{v}} = \left\langle { - 30,18,9} \right\rangle {\text{ and }}{\mathbf{u}} \times {\mathbf{v}} = \left\langle {30, - 18, - 9} \right\rangle \]
Work Step by Step
\[\begin{gathered}
{\mathbf{u}} = \left\langle {3,5,0} \right\rangle ,\,\,\,{\mathbf{v}} = \left\langle {0,3, - 6} \right\rangle \hfill \\
\hfill \\
{\text{Calculate }}{\mathbf{u}} \times {\mathbf{v}} \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = \left| {\begin{array}{*{20}{c}}
{\mathbf{i}}&{\mathbf{j}}&{\mathbf{k}} \\
3&5&0 \\
0&3&{ - 6}
\end{array}} \right| \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = \left| {\begin{array}{*{20}{c}}
5&0 \\
3&{ - 6}
\end{array}} \right|{\mathbf{i}} - \left| {\begin{array}{*{20}{c}}
3&0 \\
0&{ - 6}
\end{array}} \right|{\mathbf{j}} + \left| {\begin{array}{*{20}{c}}
3&5 \\
0&3
\end{array}} \right|{\mathbf{k}} \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = \left( { - 30 - 0} \right){\mathbf{i}} - \left( { - 18 - 0} \right){\mathbf{j}} + \left( {9 - 0} \right){\mathbf{k}} \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = - 30{\mathbf{i}} + 18{\mathbf{j}} + 9{\mathbf{k}} \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = \left\langle { - 30,18,9} \right\rangle \hfill \\
\hfill \\
{\text{Calculate }}{\mathbf{v}} \times {\mathbf{u}} \hfill \\
{\mathbf{v}} \times {\mathbf{u}} = \left| {\begin{array}{*{20}{c}}
{\mathbf{i}}&{\mathbf{j}}&{\mathbf{k}} \\
0&3&{ - 6} \\
3&5&0
\end{array}} \right| \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = \left| {\begin{array}{*{20}{c}}
3&{ - 6} \\
5&0
\end{array}} \right|{\mathbf{i}} - \left| {\begin{array}{*{20}{c}}
0&{ - 6} \\
3&0
\end{array}} \right|{\mathbf{j}} + \left| {\begin{array}{*{20}{c}}
0&3 \\
3&5
\end{array}} \right|{\mathbf{k}} \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = \left( {0 + 30} \right){\mathbf{i}} - \left( {0 + 18} \right){\mathbf{j}} + \left( {0 - 9} \right){\mathbf{k}} \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = 30{\mathbf{i}} - 18{\mathbf{j}} - 9{\mathbf{k}} \hfill \\
{\mathbf{u}} \times {\mathbf{v}} = \left\langle {30, - 18, - 9} \right\rangle \hfill \\
\end{gathered} \]
