Take a look here. (You can find almost anything you need on the internet.)
3. Let A, B and C be three non-parallel vectors in R3.
Express A x (B x C) in the form
aB + bC with scalars a and b (or alpha and beta):
(i) Explain why it is clear that A x (B x C) must be a linear combination of B and C;
(ii) Choose an orthonormal basis ijk adapted to the problem and prove it by standard properties of the vector product.
(Note: there is a way of choosing the orthonormal basis in a way which makes all the calculations very easy.)
Someone has told me use Lagrange formula...but my tutor has said not to....mmm