1. ## Vector field question

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

ÑX[fV]=fÑxV-VxÑf
V is not irrotational means:

curl(V)=U
U
non equal to zero.

f
V irrotational means:
curl(fV)=0

But:

So you get:

Then,what should I do?

2. Originally Posted by kolahalb
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.
Chose f(x,y,z)=0
What is the problem?

3. The problem is to find f(x,y,z) to prove that ÑX[fV] can be made equal to zero even if ÑX[V] is not zero.

4. Originally Posted by kolahalb
The problem is to find f(x,y,z) to prove that ÑX[fV] can be made equal to zero even if ÑX[V] is not zero.
I did! The curl of the zero vector is a zero vector. Right?

So given any irrotational vector field.
If you multiply it by f(x,y,z)=0 then it because a zero vector. Whose circulation is a zero vector. Hence the scalar function is always zero.

My construction is trivial. But there is nothing in your question which forbids me from using that.