1. The problem statement, all variables and given/known data F= <y,z,x> S is the hemisphere x^2 + y^2 + z^2 = 1, y ≥ 0, oriented in the direction of the positive y-axis. Verify Stokes' theorem. 2. Relevant equations 3. The attempt at a solution So I completed the surface integral part. I'm trying to do the line integral part of Stokes' theorem and end up with the same answer. Where I get confused is there parametrization part. I said that r(t) = <cos t, 0, sin t>, 0≤t≤2∏. Apparently that's the wrong orientation. But when I "grab" the y-axis with my thumb in the positive y-direction and curl my fingers they go from the z axis to the x-axis counter clockwise. Isn't that the CORRECT orientation? I guess what I'm asking is how do I determine the orientation when I'm using Stokes' theorem. I assume I want the same counter clockwise orientation that I do for Green's theorem.