# What is the cross product of [-1, -1, 2] and [3, 2, 5] ?

Dec 27, 2015

$- 9 \hat{i} + 11 \hat{j} + \hat{k}$

#### Explanation:

This algebraic cross product of two 3-dimensional vectors may be calculated by a matrix determinant as follows :

$\left(- 1 , - 1 , 2\right) \times \left(3 , 2 , 5\right) = | \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(- 1 , - 1 , 2\right) , \left(3 , 2 , 5\right) |$

$= \hat{i} \left(- 5 - 4\right) - \hat{j} \left(- 5 - 6\right) + \hat{k} \left(- 2 + 3\right)$

$= - 9 \hat{i} + 11 \hat{j} + \hat{k}$