# VC5.25

From Example Problems

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)

Where,let --(2)

Now,we have --(3)

Equation of the surface S1 is

Therefore, --(4)

Therefore,n=the unit normal vector to surface S1=

Now,,using (1)

= 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.