Question

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

Answer 1

The answer is `〈3,1,-5〉`

Explanation:

Let `vecu=〈1,2,1〉`

and `vecv=〈2,-1,1〉`

The cross product is given by the determinant

`∣ ((veci,vecj,veck) , (1,2,1) , (2,-1,1)) ∣`

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

`=3veci+vecj-5veck`

`vecw=〈3,1,-5〉`

Verifications, by doing the dot product

`vecw.vecu=〈3,1,-5〉.〈1,2,1〉=3+2-5=0`

`vecw.vecv〈3,1,-5〉.〈2,-1,1〉=6-1-5=0`

So, `vecw` is perpendicular to `vecu` and `vecv`