# What is the cross product of (4 i + 4 j + 2 k) and (i + j -7k)?

Dec 18, 2016

The vector is =〈-30,30,0〉

#### Explanation:

The cross product is obtained from the determinant

$| \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(4 , 4 , 2\right) , \left(1 , 1 , - 7\right) |$

$= \hat{i} \left(- 28 - 2\right) - \hat{j} \left(- 28 - 2\right) + \hat{k} \left(0\right)$

=〈-30,30,0〉

Verification

we do a dot product

〈-30,30,0〉.〈4,4,2〉=(-120+120+0=0)

〈-30,30,0〉.〈1,1,-7〉=(-30+30-0)=0