A vector function F is not irrotational.Show that it is always possible to find a scalar function f so that the function fF is irrotational.

A vector fieldVis not irrotational.Show that it is always possible to find f such that fVis irrotational.

ÑX[fV]=fÑxV-VxÑf

Vis not irrotational means:

curl(V)=Unon equal to zero.

U

fVirrotational means:

curl(fV)=0But

:curl(fV)=grad(f)xV+fcurl(V)=grad(f)xV+fUgrad(f)

So you get:

xV+fU=0grad(f)/f

xV+ U=0grad(ln(f))

xV=-U

Then,what should I do?