Question

What is the cross product of `[3,-1,2]` and `[1,-1,3]`?

Answer 1

The vector is `=〈-1,-7,-2〉`

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=〈3,-1,2〉` and `vecb=〈1,-1,3〉`

Therefore,

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

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

`=veci(-1)-vecj(7)+veck(-2)`

`=〈-1,-7,-2〉=vecc`

Verification by doing 2 dot products

`veca.vecc`

`=〈3,-1,2>.〈-1,-7,-2〉=-3+7-4=0`

`vecb.vecc`

`=〈1,-1,3〉.〈-1,-7,-2〉=-1+7-6=0`

So,

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