Answer
\[\begin{align}
& \mathbf{u}\times \mathbf{v}=-9\mathbf{i}+8.7\mathbf{j}+7\mathbf{k} \\
& \mathbf{v}\times \mathbf{u}=9\mathbf{i}-8.7\mathbf{j}-7\mathbf{k} \\
\end{align}\]
Work Step by Step
\[\begin{align}
& \mathbf{u}=2\mathbf{i}-10\mathbf{j}+15\mathbf{k},\text{ }\mathbf{v}=0.5\mathbf{i}+\mathbf{j}-0.6\mathbf{k} \\
& \text{Calculate the cross product }\mathbf{u}\times \mathbf{v} \\
& \mathbf{u}\times \mathbf{v}=\left| \begin{matrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
2 & -10 & 15 \\
0.5 & 1 & -0.6 \\
\end{matrix} \right| \\
& \mathbf{u}\times \mathbf{v}=\left| \begin{matrix}
-10 & 15 \\
1 & -0.6 \\
\end{matrix} \right|\mathbf{i}-\left| \begin{matrix}
2 & 15 \\
0.5 & -0.6 \\
\end{matrix} \right|\mathbf{j}+\left| \begin{matrix}
2 & -10 \\
0.5 & 1 \\
\end{matrix} \right|\mathbf{k} \\
& \mathbf{u}\times \mathbf{v}=\left( 6-15 \right)\mathbf{i}-\left( -1.2-7.5 \right)\mathbf{j}+\left( 2+5 \right)\mathbf{k} \\
& \mathbf{u}\times \mathbf{v}=-9\mathbf{i}+8.7\mathbf{j}+7\mathbf{k} \\
& \text{Calculate the cross product }\mathbf{v}\times \mathbf{u} \\
& \mathbf{v}\times \mathbf{u}=\left| \begin{matrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
0.5 & 1 & -0.6 \\
2 & -10 & 15 \\
\end{matrix} \right| \\
& \mathbf{v}\times \mathbf{u}=\left| \begin{matrix}
1 & -0.6 \\
-10 & 15 \\
\end{matrix} \right|\mathbf{i}-\left| \begin{matrix}
0.5 & -0.6 \\
2 & 15 \\
\end{matrix} \right|\mathbf{j}+\left| \begin{matrix}
0.5 & 1 \\
2 & -10 \\
\end{matrix} \right|\mathbf{k} \\
& \mathbf{v}\times \mathbf{u}=\left( 15-6 \right)\mathbf{i}-\left( 7.5+1.2 \right)\mathbf{j}+\left( -5-2 \right)\mathbf{k} \\
& \mathbf{v}\times \mathbf{u}=9\mathbf{i}-8.7\mathbf{j}-7\mathbf{k} \\
\end{align}\]
