Cross product by epsilon ijk method

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Homework Help Overview

The original poster attempts to calculate the expression Ax(BxC) using the epsilon ijk method, indicating a focus on vector operations and the Levi-Civita symbol. The problem involves manipulating indices and applying the properties of the epsilon symbol in the context of vector multiplication.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster begins with an expression involving the Levi-Civita symbol and vectors A, B, and C, but expresses difficulty in progressing after setting up the equation. Some participants suggest referring to external resources for collapsing products of the symbol, while others emphasize the need for the original poster to engage more deeply with the material.

Discussion Status

The discussion is ongoing, with participants providing guidance on resources and encouraging the original poster to apply relevant relations from the suggested material. There is no explicit consensus on a solution, but a direction for further exploration has been indicated.

Contextual Notes

The original poster's approach relies on specific mathematical properties and symbols, which may not be fully understood by all participants. There is an implied expectation of prior knowledge regarding the Kronecker delta and vector multiplication rules.

physiker99
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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.
 
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I know Wikipedia, but if someone would bother to actually solve the question, I will be glad.
 
physiker99 said:
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?
 

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