Question

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

Answer 1

The cross product is `=〈-3,-13,-2〉`

Explanation:

The cross product of two vectors `vecu=〈u_1,u_2,u_3〉`
and `vecv=〈v_1,v_2,v_3〉` is the determinant
`∣((veci,vecj,veck),(u_1,u_2,u_3),(v_1,v_2,v_3))∣`

=`veci(u_2v_3-u_3v_2)-vecj(u_1v_3-u_3v_1)+veck(u_1v_2-u_2v_1)`

Here we have `vecu=〈3,-1,2〉` and `vecv=〈-2,0,3〉`

So the cross product is `vecw=〈veci(-3)-vecj(-13)+veck(-2〉`
`=〈-3,-13,-2〉`
To check, we verify that the dot products are `=0`
`vecw.vecu=(-9+13-4)=0`
`vecw.vecv=(6+0-6)=0`