If $u\vec{f} = \nabla v$ where $u$ and $v$ are scalar fields and $\vec{f}$ is a vector then prove that $\vec{f}.\text{curl F} = 0$
So, $u\vec{f} = \nabla v$ Taking Curl both sides we get:
$\nabla u \times f + u \nabla \times f =0$ Now if I take dot product with $f$ I get:
$f.\left(\nabla u \times f\right) + u f.\left(\nabla \times f\right) = 0$
After This step I am stuck, Can anyone tell me how should I proceed ?
Thank you.