Answer
\[\left\langle -8,-40,16 \right\rangle \]
Work Step by Step
\[\begin{align}
& \text{Let }\mathbf{u}=\left\langle 8,0,4 \right\rangle \text{ and }\mathbf{v}=\left\langle -8,2,1 \right\rangle \\
& \text{A vector orthogonal to }\mathbf{u}\text{ and }\mathbf{v}\text{ is parallel to }\mathbf{u}\times \mathbf{v}\text{. One such } \\
& \text{orthogonal vector is} \\
& \mathbf{u}\times \mathbf{v}=\left| \begin{matrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
8 & 0 & 4 \\
-8 & 2 & 1 \\
\end{matrix} \right| \\
& \mathbf{u}\times \mathbf{v}=\left| \begin{matrix}
0 & 4 \\
2 & 1 \\
\end{matrix} \right|\mathbf{i}-\left| \begin{matrix}
8 & 4 \\
-8 & 1 \\
\end{matrix} \right|\mathbf{j}+\left| \begin{matrix}
8 & 0 \\
-8 & 2 \\
\end{matrix} \right|\mathbf{k} \\
& \mathbf{u}\times \mathbf{v}=\left( 0-8 \right)\mathbf{i}-\left( 8+32 \right)\mathbf{j}+\left( 16+0 \right)\mathbf{k} \\
& \mathbf{u}\times \mathbf{v}=-8\mathbf{i}-40\mathbf{j}+16\mathbf{k} \\
& \mathbf{u}\times \mathbf{v}=\left\langle -8,-40,16 \right\rangle \\
\end{align}\]
