# What is the cross product of [3,2, 5] and [0,8,5] ?

Dec 8, 2015

$= - 30 \hat{i} - 15 \hat{j} + 24 \hat{k}$

#### Explanation:

In 3 dimensions, as these vectors are, we may use a determinant of a matrix system as follows to evaluate the cross product :

$\left(3 , 2 , 5\right) \times \left(0 , 8 , 5\right) = | \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(3 , 2 , 5\right) , \left(0 , 8 , 5\right) |$

$= \left(10 - 40\right) \hat{i} - \left(15 - 0\right) \hat{j} + \left(24 - 0\right) \hat{k}$

$= - 30 \hat{i} - 15 \hat{j} + 24 \hat{k}$