Question

What is the cross product of `[-1, 2, 3]` and `[-8, 5, 1]`?

Answer 1

The cross product is `=〈-13,-23,11〉`

Explanation:

If we have 2 vectors `vecu=〈u_1,u_2,u_3〉`
and `vecv=〈v_1,v_2,v_3〉`
The cross product is given by 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=〈-1,2,3〉` and `vecv=〈-8,5,1〉`
so the cross product is `〈(2-15),-(-1+24),(-5+16)〉`
`=〈-13,-23,11〉`