Question

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

Answer 1

The answer is `=〈18,9,5〉`

Explanation:

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

`| (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=〈-1,2,0〉` and `vecb=〈-3,1,9〉`

Therefore,

`| (veci,vecj,veck), (-1,2,0), (-3,1,9) |`

`=veci| (2,0), (1,9) | -vecj| (-1,0), (-3,9) | +veck| (-1,2), (-3,1) |`

`=veci(18)-vecj(-9)+veck(-1+6)`

`=〈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,

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