Question

What is the cross product of `[2,4,5]` and `[0,1,2]`?

Answer 1

The cross product is `〈3,-4,2〉`

Explanation:

The cross product of 2 vectors `vecu=〈u_1,u_2,u_3〉` and `vecv=〈v_1,v_2,v_3〉` is given by

`vecu`x`vecv` `=〈u_2v_3-u_3v_2,u_3v_1-u_1v_3,u_1v_2-u_2v_1〉`
This vector is perpendicular to `vecu` and `vecv`

So the cross product of `〈2,4,5〉` and `〈0,1,2〉` is `〈3,-4,2〉`

Verification by making the dot product
`〈2,4,5〉.〈3,-4,2〉=6-16+10=0`
and `〈0,1,2〉.〈3,-4,2〉=0-4+4=0`

As both dot products are `=0` so the vector is perpendicular to the other 2 vectors