Question

What is the cross product of `[3, 1, -4]` and `[3, -4, 2]`?

Answer 1

The vector is `=〈-14,-18,-15〉`

Explanation:

Let `vecu=〈3,1,-4〉` and `vecv=〈3,-4,2〉`

The cross product is given by the determinant

`vecu` x `vecv` `= | (veci,vecj,veck), (3,1,-4), (3,-4,2) |`

`= veci| (1,-4), (-4,2) | -vecj | (3,-4), (3,2) | +veck | (3,1), (3,-4) |`

`=veci(2-16)+vecj(-6-12)+veck(-12-3)`

`=vecw=〈-14,-18,-15〉`

Verification, the dot products must de `0`

`vecu.vecw=〈3,1,-4〉.〈-14,-18,-15〉=(-42-18+60)=0`

`vecv.vecw=〈3,-4,2〉.〈-14,-18,-15〉=(-42+72-30)=0`

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