Question

a) prove the identity:
Ax(BXC)=B(A*C)-C(A*B)

A,B,C vectors
x- cross product
*-dot product

b) use part a) to prove that cross product is not associative.

Answer 1

google vector triple product and you will find lots of proofs. One that is relatively straightforward is at

http://www.msci.memphis.edu/faculty/dwiggins/files/triplecross.htm

You already know that AxB = -BxA, so that will help in the part (b).