# What is the cross product of <3,-6,4> and <-1,-1,2>?

Jul 13, 2017

$< 3 , - 6 , 4 > \times < - 1 , - 1 , 2 > = < - 8 , - 10 , - 9 >$

#### Explanation:

We can use the notation:

$\setminus \setminus \setminus \setminus \setminus \left(\begin{matrix}3 \\ - 6 \\ 4\end{matrix}\right) \times \left(\begin{matrix}- 1 \\ - 1 \\ 2\end{matrix}\right) = | \left(\underline{\hat{i}} , \underline{\hat{j}} , \underline{\hat{k}}\right) , \left(3 , - 6 , 4\right) , \left(- 1 , - 1 , 2\right) |$

$\text{ } = | \left(- 6 , 4\right) , \left(- 1 , 2\right) | \underline{\hat{i}} - | \left(3 , 4\right) , \left(- 1 , 2\right) | \underline{\hat{j}} + | \left(3 , - 6\right) , \left(- 1 , - 1\right) | \underline{\hat{k}}$

$\text{ } = \left(- 12 - \left(- 4\right)\right) \underline{\hat{i}} - \left(6 - \left(- 4\right)\right) \underline{\hat{j}} + \left(- 3 - 6\right) \underline{\hat{k}}$

$\text{ } = - 8 \underline{\hat{i}} - 10 \underline{\hat{j}} - 9 \underline{\hat{k}}$
$\text{ } = \left(\begin{matrix}- 8 \\ - 10 \\ - 9\end{matrix}\right)$