I'm wondering if anyone knows of a vector identity to expand the following expression:
$$ \nabla\times\left(\phi\nabla\times\psi\boldsymbol{A}\right) $$
where $\boldsymbol{A}$ is a vector field, and $\phi$ and $\psi$ are scalar fields. All three fields vary with position. Is there a way to use the $\nabla\times\left(\boldsymbol{A}\times\boldsymbol{B}\right)$ identity? I don't think I can just use a substitution.
Thanks in advance