Here the curve C is given by or which is the curve of intersection of the sphere and the plane
Since the center of the sphere (a,a,0)lies on the plane
C is a circle lying on the plane and radius . Let S1 be taken as the region bounded by this circle C.
Now,we have --(1)
Now,we have --(3)
Equation of the surface S1 is
Therefore,n=the unit normal vector to surface S1=
= by Stokes'theorm
=,by (3) and (4)
Here,the sense of description of the circle C,namely,starting from the point (2a,0,0) and going below the xy-plane,ensures that the positive direction of n is i+j.