Chapter 17.8, Problem 31E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a.    If ▿ · F = 0 at all points of a region D. then F · n = 0 at all points of the boundary of D.

b.    If ${\displaystyle {\iint }_{S}F\cdot ndS}=0$ on all closed surfaces in ¡³, then F is constant.

c.    If |F| < 1, then $\left|{\displaystyle {\iint }_D\nabla \cdot FdV}\right|$ is less than the area of the surface of D.