# What is the cross product of <3 ,1 ,-6 > and <-2 ,1 , 8 >?

Apr 20, 2018

$< 14 , - 12 , 5 >$

#### Explanation:

we want

$< 3 , 1 , - 6 > \times < - 2 , 1 , 8 >$

this is found by calculating the determinant

$| \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(3 , 1 , - 6\right) , \left(- 2 , 1 , 8\right) |$

expand by row 1

$\hat{i} | \left(1 , - 6\right) , \left(1 , 8\right) | - \hat{j} | \left(3 , - 6\right) , \left(- 2 , 8\right) | + \hat{k} | \left(3 , 1\right) , \left(- 2 , 1\right) |$

$= \hat{i} \left(8 - - 6\right) - \hat{j} \left(24 - 12\right) + \hat{k} \left(3 - - 2\right)$

$14 \hat{i} - 12 \hat{j} + 5 \hat{k}$

$= < 14 , - 12 , 5 >$