- #1
tigger88
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Homework Statement
Using the Einstein summation convention, prove:
A[tex]\bullet[/tex]B[tex]\times[/tex]C = C[tex]\bullet[/tex]A[tex]\times[/tex]B
Homework Equations
The Attempt at a Solution
I tried to follow an example from my notes, but I don't entirely understand it. Would it be possible to find out if what I've done (below) is correct, or where I went wrong?
(B[tex]\times[/tex]C)[tex]_{i}[/tex] = [tex]\epsilon[/tex][tex]_{ijk}[/tex]B[tex]_{j}[/tex]C[tex]_{k}[/tex]
(A[tex]\bullet[/tex]B[tex]\times[/tex]C)[tex]_{i}[/tex] = [tex]\epsilon[/tex][tex]_{ijk}[/tex]A[tex]_{i}[/tex]B[tex]_{j}[/tex]C[tex]_{k}[/tex]
= [tex]\epsilon[/tex][tex]_{kij}[/tex]A[tex]_{i}[/tex]B[tex]_{j}[/tex]C[tex]_{k}[/tex]
=C[tex]\bullet[/tex]A[tex]\times[/tex]B
Thanks!
PS. I'm not very familiar with Latex and couldn't get the symbols to line up properly.. sorry! They should all be subscripts.