Stoke's Theorem Sphere and Plane

[IniquiTrance]

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

Find the flux of the curl of F: \vec{F}=<yz,xz,xy>

Over S defined by:

Sphere: x^{2}+y^{2}+z^{2}=1

Where x+y+z \geq 1

2. Relevant equations



3. The attempt at a solution

I know I have to use Stoke's theorem to evaluate the line integral counterclockwise around the circular path formed by the intersection of:

x^{2}+y^{2}+z^{2}=1

and

x+y+z = 1

I'm having trouble setting up this line integral. Any insights would be greatly appreciated.