Proving the Irrotational Property of Vector Fields with an Example Solution

[neelakash]

Homework Statement

A vector field V is not irrotational.Show that it is always possible to find f such that fV is irrotational.

Homework Equations

The Attempt at a Solution

\nablax[fV]=f\nablaxV-Vx\nablaf
I have to equate the LHS to zero.But then,how can I extract f out of the resulting equation?
Please help

 

[neelakash]

I don't know why that \nabla didn't work.Please bear with this problem and help me.