Finding a Plane with Zero Circulation for a Given Vector Field

[bfr]

Homework Statement

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 [tex]\oint_{C}[/tex]f dot dX = 0 for any closed curve C lying in the plane.

Homework Equations

http://img187.imageshack.us/img187/291/1fdf437d8e18a23191b63dfnj8.png

The Attempt at a Solution

With Stokes' theorem and a bit of algebra I get: [tex]\int\int[/tex] ( 1,2,5) dot [tex]\nabla[/tex]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?

 

[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.

 

[bfr]

Er, oops .

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

 

[Dick]

Er, oops .

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

Seems so to me.