Cross product by epsilon ijk method

[physiker99]

Homework Statement

I need to calculate Ax(BxC) -A, B, C are vectors, apart from bac-cab rule, I need to get it by epsilon ijk -Following I will note it by e(ijk).

Homework Equations

I expect answerer to know kronecker delta equation and vector multiplications.

The Attempt at a Solution

e(ijk)*A(i)*(B*C)(j)
= e(ijk)*A(i)

(BxC)(j) = e(mjn)B(n)C(m)

After that part I'm stuck. As you can see below, I rotate the ijk's and mjn's to match j's at the end, but I fail.

e(ijk)*A(k)*e(mjn)*B(n)*C(m)

Can you help me after that?
Lettters in parantheses (i, j, k, m, n) are supposed to indicate the indices.

 

[vela]

Check out this page:

http://en.wikipedia.org/wiki/Levi-Civita_symbol

It tells you how to collapse products of the symbol. That's what you need to solve the problem.

 

[physiker99]

I know Wikipedia, but if someone would bother to actually solve the question, I will be glad.

 

[cristo]

I know Wikipedia, but if someone would bother to actually solve the question, I will be glad.

I'm afraid that's not how things work around here-- if you come here asking a question you should be prepared to put in the work to find the solution. Homework helpers are here to help guide you to a solution.

So, can you apply some of the relations on the page vela showed you to your problem?