the problem is as following
Use stokes theorem to evaluate $\oint F.dr$ where,
F = (-2Z) i + (X) j - (X) k , C is the ellipse $X^2 + Y^2 = 1 $ and $ Z = Y + 1 $
my solution is to get $curl F $ (already got) then to get the unit vector normal to the resulting ellipse of the intersection of the cylinder and the plane ... my main problem is to get to an equation of the ellipse which I can use to get $grad$ for this equation (normal to that surface and divide it by its magnitude
So how to get the normal to the ellipse ?