# Force Fields and Curl

1. Jan 20, 2009

### bfr

1. The problem statement, all variables and given/known data

Suppose that f is a vector field such that curl f=(1,2,5) at every point in R^3. Find an equation of a plane through the origin with the property that $$\oint_{C}$$f dot dX = 0 for any closed curve C lying in the plane.

2. Relevant equations

3. The attempt at a solution

With Stokes' theorem and a bit of algebra I get: $$\int\int$$ ( 1,2,5) dot $$\nabla$$g dy dx) = 0 . So, 1*dx+2*dy+3*dz=0; let dx=1; let dy=1; dz=-1. The resulting plane is x+y-z=0. Is this right?

2. Jan 20, 2009

### Dick

You want curl(F)=(1,2,5) to be normal to the plane, right? I don't think that gives you x+y-z=0.

3. Jan 20, 2009

### bfr

Er, oops .

Then I guess x+2y+5z=0 would simply be the answer?

4. Jan 20, 2009

### Dick

Seems so to me.