# What is the cross product of <8, 4 ,-2 > and <-1, -4, 1>?

Jan 19, 2017

The answer is =〈-4,-6,-28〉

#### Explanation:

The cross product of 2 vectors is calculated with the determinant

$| \left(\vec{i} , \vec{j} , \vec{k}\right) , \left(d , e , f\right) , \left(g , h , i\right) |$

where 〈d,e,f〉 and 〈g,h,i〉 are the 2 vectors

Here, we have veca=〈8,4,-2〉 and vecb=〈-1,-4,1〉

Therefore,

$| \left(\vec{i} , \vec{j} , \vec{k}\right) , \left(8 , 4 , - 2\right) , \left(- 1 , - 4 , 1\right) |$

$= \vec{i} | \left(4 , - 2\right) , \left(- 4 , 1\right) | - \vec{j} | \left(8 , - 2\right) , \left(- 1 , 1\right) | + \vec{k} | \left(8 , 4\right) , \left(- 1 , - 4\right) |$

$= \vec{i} \left(4 - 8\right) - \vec{j} \left(8 - 2\right) + \vec{k} \left(- 32 + 4\right)$

=〈-4,-6,-28〉=vecc

Verification by doing 2 dot products

〈-4,-6,-28〉.〈8,4,-2〉=-32-24+56=0

〈-4,-6,-28〉.〈-1,-4,1〉=4+24-28=0

So,

$\vec{c}$ is perpendicular to $\vec{a}$ and $\vec{b}$