- #1

- 3,003

- 3

## Homework Statement

I am supposed to verify that

[tex]\nabla\cdot(\mathbf{u}\times\mathbf{v}) = \mathbf{v}\cdot\nabla\times\mathbf{u} - \mathbf{u}\cdot\nabla\times\mathbf{v}\qquad(1)[/itex]

I want to use index notation (and I think I am supposed to, though it does not say to explicitly) to verify this.

I know that we can write [itex]\mathbf{w}=\mathbf{u}\times\mathbf{v}[/itex] as [itex]w_i = \epsilon_{ijk}u_jv_k[/itex] hence we would write:

[tex]\nabla\cdot(\mathbf{u}\times\mathbf{v}) = \partial{}_i\epsilon_{ijk}u_jv_k[/tex]

Now I am trying to figure out how I would get a difference to show up in this to match the right hand side of (1). I know that the point of index notation is that it is essentially all just scalar algebra ... but I could use a hint on this one.