# What is the cross product of <-1, 2 ,0 > and <-3 ,1 ,9 >?

Feb 20, 2017

The answer is =〈18,9,5〉

#### Explanation:

The vector perpendicular to 2 vectors is calculated with the determinant (cross product)

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

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

Here, we have veca=〈-1,2,0〉 and vecb=〈-3,1,9〉

Therefore,

$| \left(\vec{i} , \vec{j} , \vec{k}\right) , \left(- 1 , 2 , 0\right) , \left(- 3 , 1 , 9\right) |$

$= \vec{i} | \left(2 , 0\right) , \left(1 , 9\right) | - \vec{j} | \left(- 1 , 0\right) , \left(- 3 , 9\right) | + \vec{k} | \left(- 1 , 2\right) , \left(- 3 , 1\right) |$

$= \vec{i} \left(18\right) - \vec{j} \left(- 9\right) + \vec{k} \left(- 1 + 6\right)$

=〈18,9,5〉=vecc

Verification by doing 2 dot products

〈-1,2,0>.〈18,9,5〉=-18+18=0

〈-3,1,9〉.〈18,9,5〉=-54+9+45=0

So,

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