Question

What is the cross product of `[-3, 1, -1]` and `[0,1,2]`?

Answer 1

The vector is `=〈3,6,-3〉`

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,-1〉` and `vecb=〈0,1,2〉`

Therefore,

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

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

`=veci(1*2+1*1)-vecj(-3*2+0*1)+veck(-3*1-0*1)`

`=〈3,6,-3〉=vecc`

Verification by doing 2 dot products

`〈3,6,-3〉.〈-3,1,-1〉=-3*3+6*1+3*1=0`

`〈3,6,-3〉.〈0,1,2〉=3*0+6*1-3*2=0`

So,

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