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

Oct 28, 2017

$- 3 \hat{i} + \hat{j} - \hat{k}$

#### Explanation:

$\left[1 , - 2 , - 1\right] \times \left[0 , - 1 , 1\right]$

can be calculated by the determinate

$| \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(1 , - 2 , - 1\right) , \left(0 , - 1 , 1\right) |$

expanding

$\hat{i} | \left(- 2 , - 1\right) , \left(- 1 , 1\right) | - \hat{j} | \left(1 , - 1\right) , \left(0 , 1\right) | + \hat{k} | \left(1 , - 2\right) , \left(0 , - 1\right) |$

$= \hat{i} \left(- 2 - 1\right) + \hat{j} \left(1 - 0\right) + \hat{k} \left(- 1 - 0\right)$

$= - 3 \hat{i} + \hat{j} - \hat{k}$