Recent content by johnnydoejr

Thanks, that does it.

Thought I had a breakthrough after referencing another forum post. Was able to work through this: \begin{align*} [(A\times B)\times(C\times D)]_{i} &= \varepsilon_{ijk}(A\times B)_{j}(C\times D)_{k} \\ &= \varepsilon_{ijk} \varepsilon_{jmn} A_{m}B_{n} \varepsilon_{kpq} C_{p}D_{q} \\ &=...

Yes, [a,b,c]=a⋅(b×c). I'm sure it will be helpful, but only after I can get past the initial steps. I'm aware of the Kronecker delta identity you refer to, I used it to prove the scalar quadruple product/Lagrange's Identity as part of the same assignment. I don't doubt that that will be...

I'm asked to prove the following using Levi-Civita/index notation: (\mathbf{a \times b} )\mathbf{\times} (\mathbf{c}\times \mathbf{d}) = [\mathbf{a,\ b, \ d}] \mathbf c - [\mathbf{a,\ b, \ c}] \mathbf d \ I'm able to prove it using triple product identities, but I'm completely stuck...