Question

What is the cross product of `[1, 4, -2]` and `[2, -1, 1]`?

Answer 1

The result is `=〈2,-5,-9〉`

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=〈1,4,-2〉` and `vecb=〈2,-1,1〉`

Therefore,

`| (veci,vecj,veck), (1,4,-2), (2,-1,1) |`

`=veci| (4,-2), (-1,1) | -vecj| (1,-2), (2,1) | +veck| (1,4), (2,-1) |`

`=veci(2)-vecj(5)+veck(-9)`

`=〈2,-5,-9〉=vecc`

Verification by doing 2 dot products

`veca.vecc`

`=〈1,4,-2>.〈2,-5,-9〉=2-20+18=0`

`vecb.vecc`

`=〈2,-1,1〉.〈2,-5,-9〉=4+5-9=0`

So,

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