Let F(r) = r / ||r||2 = (xi + yj) / (x2 + y2). (a) Show that

Question:

Let F(r) = r / ||r||2 = (xi + yj) / (x2 + y2).
(a) Show that (c F ( n ds = 2(, where C is the circle centered at the origin of radius a and n = (xi + yj) / (x2 + y2 is the exterior unit normal to C.
(b) Show that div F = 0.
(c) Explain why the results of parts (a) and (b) do not contradict the vector form of Green's Theorem.
(d) Show that if C is a smooth simple closed curve then (c F ( n ds equals 2( or 0 accordingly as the origin in inside or outside C?