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

Apr 17, 2016

$A X B = - 2 \hat{i} - \hat{k}$

#### Explanation:

$A = \left[2 , 1 , - 4\right]$

$B = \left[- 1 , - 1 , 2\right]$

$A X B = \hat{i} \left(1 \cdot 2 - 1 \cdot 4\right) - \hat{j} \left(2 \cdot 2 - 4 \cdot 1\right) + \hat{k} \left(2 \cdot \left(- 1\right) + 1 \cdot 1\right)$

$A X B = \hat{i} \left(2 - 4\right) - \hat{j} \left(4 - 4\right) + \hat{k} \left(- 2 + 1\right)$

$A X B = - 2 \hat{i} - 0 \hat{j} - \hat{k}$

$A X B = - 2 \hat{i} - \hat{k}$