1. Prove that the cross product is non-associative.

So basically I want to prove that

. Now I probably just need to find a counterexample right? So I can just use

and

?

Mr F says: Yep. But I have a feeling that proof by counter-example wasn't the sort of proof the folks who set the question had in mind .....
2. Prove that

Just using definitions, I get

Mr F says: gives a vector perpendicular to and ...... So the dot product of this vector with will obviously be zero since it's perpendicular to ...