# What is the cross product of <-3, -1, 8 > and <2,-4, -9 >?

Aug 17, 2016

$\left(\begin{matrix}41 \\ - 11 \\ 14\end{matrix}\right)$

#### Explanation:

Let

$\vec{u} = - 3 \vec{i} - \vec{j} + 8 \vec{k}$

$\vec{v} = 2 \vec{i} - 4 \vec{j} - 9 \vec{k}$

$\vec{u} \times \vec{v} = \left[\begin{matrix}\vec{i} & \vec{j} & \vec{k} \\ - 3 & - 1 & 8 \\ 2 & - 4 & - 9\end{matrix}\right]$

$= \vec{i} \left[\begin{matrix}- 1 & 8 \\ - 4 & - 9\end{matrix}\right] - \vec{j} \left[\begin{matrix}- 3 & 8 \\ 2 & - 9\end{matrix}\right] + \vec{k} \left[\begin{matrix}- 3 & - 1 \\ 2 & - 4\end{matrix}\right]$

$= \vec{i} \left(9 + 32\right) - \vec{j} \left(27 - 16\right) + \vec{k} \left(12 + 2\right)$

$\therefore \vec{u} \times \vec{v} = 41 \vec{i} - 11 \vec{j} + 14 \vec{k}$