(949, #19) Evaluate

where F(x,y,z) = < x, y, z > and S is the sphere x2 + y2 + z2 = 9.

Solution: Use the spherical-coordinate parametric representation:

x(u,v) = 3 sin(u) cos(v), y(u,v) = 3 sin(u) sin(v), z(u,v) = 3 cos(u).

Then (see page 935)

Consequently