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

Jan 27, 2016

$\left[6 , 14 , - 11\right]$

#### Explanation:

Since cross product is distributive, you can "expand" it

$\left(- \hat{i} + 2 \hat{j} + 2 \hat{k}\right) \times \left(4 \hat{i} + 3 \hat{j} + 6 \hat{k}\right)$

$= \left(- \hat{i}\right) \times \left(4 \hat{i}\right) + \left(- \hat{i}\right) \times \left(3 \hat{j}\right) + \left(- \hat{i}\right) \times \left(6 \hat{k}\right)$
$+ \left(2 \hat{j}\right) \times \left(4 \hat{i}\right) + \left(2 \hat{j}\right) \times \left(3 \hat{j}\right) + \left(2 \hat{j}\right) \times \left(6 \hat{k}\right)$
$+ \left(2 \hat{k}\right) \times \left(4 \hat{i}\right) + \left(2 \hat{k}\right) \times \left(3 \hat{j}\right) + \left(2 \hat{k}\right) \times \left(6 \hat{k}\right)$

$= 0 - 3 \hat{k} + 6 \hat{j}$
$- 8 \hat{k} + 0 + 12 \hat{i}$
$+ 8 \hat{j} - 6 \hat{i} + 0$

$= 6 \hat{i} + 14 \hat{j} - 11 \hat{k}$