# What is the cross product of [-3,0,1] and [1,-2,3] ?

Jul 7, 2016

$= 2 \vec{i} + 10 \vec{j} + 6 \vec{k}$
$\left[\begin{matrix}\vec{i} & \vec{j} & \vec{k} \\ - 3 & 0 & 1 \\ 1 & - 2 & 3\end{matrix}\right] = \vec{i} \left[\begin{matrix}0 & 1 \\ - 2 & 3\end{matrix}\right] - \vec{j} \left[\begin{matrix}- 3 & 1 \\ 1 & 3\end{matrix}\right] + \vec{k} \left[\begin{matrix}- 3 & 0 \\ 1 & - 2\end{matrix}\right]$
$= \vec{i} \left(0 \cdot 3 - 1 \cdot \left(- 2\right)\right) - \vec{j} \left(\left(- 3\right) \cdot 3 - 1 \cdot 1\right) + \vec{k} \left(\left(- 3\right) \cdot \left(- 2\right) - 0 \cdot 1\right)$
$= 2 \vec{i} + 10 \vec{j} + 6 \vec{k}$