Finding Area of L using Stokes Theorem

[asi123]

Homework Statement

Hey.
I need to find the circulation of F through out the line L.
I know I need to use stokes theorem, the problem is, how do I find the area of L?
I mean, I know the intersection line of the sphere and the plot looks like an ellipse on the XY surface, but how do I find the boundaries? should I switch to polar?

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

I need to find the circulation of F through out the line L.
I know I need to use stokes theorem, the problem is, how do I find the area of L?
I mean, I know the intersection line of the sphere and the plot looks like an ellipse on the XY surface, but how do I find the boundaries? should I switch to polar?

Hi asi123!

No, it's not an ellipse:

L is the intersection of x² + y² + z² = 6 and 3x - 4y - z = 0,

which is the intersection of a sphere with a plane,

so it's a circle.

And the plane goes through the origin, which is also the centre of the sphere.

Does that help?