Question

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

Answer 1

The cross product is `=〈-1,2,-1〉`

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=〈-1,0,1〉` and `vecb=〈0,1,2〉`

Therefore,

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

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

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

`=〈-1,2,-1〉=vecc`

Verification by doing 2 dot products

`〈-1,2,-1〉.〈-1,0,1〉=1+0-1=0`

`〈-1,2,-1〉.〈0,1,2〉=0+2-2=0`

So,

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