- #1
center o bass
- 560
- 2
Hello! I'm want to prove a vector identity for
[tex](\nabla \times \vec{A}) \times \vec A[/tex]
using the familiar method of levi-civita symbols and the identity
[tex]\epsilon_{kij}\epsilon{kmn} = \delta_{im}\delta_{jn} - \delta_{in}\delta{jm}[/tex],
but I don't seem to come up with any usefull answer. I end up with that
[tex][(\nabla \times \vec{A}) \times \vec A]_k = (\partial_j A_k)A_j - (\partial_k A_j)A_j[/tex]
, which doesn't seem to reduce something familiar in terms of vectors and vector operators. Any idea how I might get there?
[tex](\nabla \times \vec{A}) \times \vec A[/tex]
using the familiar method of levi-civita symbols and the identity
[tex]\epsilon_{kij}\epsilon{kmn} = \delta_{im}\delta_{jn} - \delta_{in}\delta{jm}[/tex],
but I don't seem to come up with any usefull answer. I end up with that
[tex][(\nabla \times \vec{A}) \times \vec A]_k = (\partial_j A_k)A_j - (\partial_k A_j)A_j[/tex]
, which doesn't seem to reduce something familiar in terms of vectors and vector operators. Any idea how I might get there?