4. (a) Prove that if F is a conservative vector field in domain D, then (closed integral) F.dr = 0 for every piece wise smooth, closed curve C.

(b) Prove that is a vector orthogonal to the surface (x, y, z) = c, where c is a constant.

(c) Express the volume of D as a triple integral using spherical coordinates where D is the region in R³ that lies inside the sphere x ² + y ² + z ² = 2 above the plane z = 1. [Do not evaluate the integral.