Question

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

Answer 1

The answer is `=〈20,6,11〉`

Explanation:

The cross product is calculated with the determinant

`| (veci,vecj,veck), (d,e,f), (g,h,i) |`

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

Here, we have `veca=〈3,1,-6〉` and `vecb=〈-2,3,2〉`

Therefore,

`| (veci,vecj,veck), (3,1,-6), (-2,3,2) |`

`=veci| (1,-6), (3,2) | -vecj| (3,-6), (-2,2) | +veck| (3,1), (-2,3) |`

`=veci(20)-vecj(-6)+veck(11)`

`=〈20,6,11〉=vecc`

Verification by doing 2 dot products

`〈20,6,11〉.〈3,1,-6〉=60+6-66=0`

`〈20,6,11〉.〈-2,3,2〉=-40+18+22=0`

So,

`vecc` is perpendicular to `veca` and `vecb`