R^3/Cross product/Computation/1/Example

The cross product of the vectors ${}{\begin{pmatrix}5\\8\\-2\end{pmatrix}},{\begin{pmatrix}3\\4\\1\end{pmatrix}}\in \mathbb {R} ^{3}$ is

${}{\begin{pmatrix}5\\8\\-2\end{pmatrix}}\times {\begin{pmatrix}3\\4\\1\end{pmatrix}}={\begin{pmatrix}8\cdot 1-4\cdot (-2)\\-5\cdot 1-2\cdot 3\\5\cdot 4-8\cdot 3\end{pmatrix}}={\begin{pmatrix}16\\-11\\-4\end{pmatrix}}\,.$