How to approach a cross product question

[gregi_2]

TL;DR Summary

I am hoping for advice on how to approach a what I assume to be cross product related problem that I have never encountered before

I am beginning this new general physics course and I have encountered a question involved with what I assume to be cross products, a topic that I have very little experience with. I am not looking for a direct answer to the problem but advice on what steps should be taken in order to learn how to answer the problem. The problem is as follows,

Demonstrate the following relationship: a x (b x c) = (a · c)b - (a · b)c
Starting from this relationship derive expressions for the following
(a x b) · (c x d)
(a x b)^2

 

[etotheipi]

You should write out the vectors in terms of their components! There are quite a few tricks to make the process simpler, like using summation convention, Kroneker deltas and Levi-Cevita symbols, knowing a few cute identities, but you'll get there nonetheless.

 

[fresh_42]

I am not looking for a direct answer to the problem but advice on what steps should be taken in order to learn how to answer the problem.

If you find the time, then https://arxiv.org/pdf/1205.5935.pdf is a recommendable essay to study the geometric concepts which are used in physics.