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## Homework Statement

Prove using the Levi-Civita Tensor/Kroenecker Delta that:

(AxB)x(CxD) = (A.BxD).C-(A.BxC).D

## Homework Equations

εіјkεimn = δjmδkn – δjnδkm (where δij = +1 when i = j and 0 when i ≠ j)

## The Attempt at a Solution

if E = (AxB) then Ei = εіјkAjBk, and

if F = (CxD) then Fm = εimnCnDi

from this point I'm a little confused as I'm not sure if I have to find the cross product of (ExF) using the summation notation, or if I can now relate these via the Kroenecker delta relationship given. I feel I am missing a step as there are 3 cross product relationships and I would greatly appreciate some help here as the only examples I can track down deal with 2 cross product relationships.

Thanks very much in advance

PS

Apologies for the the lack of proper subscripts but that's a problem for another day