Assume that (r) and |G(r)| both go to zero faster than 1/r as r . (a) Let F = and G =

Assume that ϕ(r) and |G(r)| both go to zero faster than 1/r as r →∞.

(a) Let F = ∇ϕ and ∇ · G = 0. Show that ∫ d³r F · G = 0.

(b) Let F = ∇ϕ and∇ ×G = 0. Show that ∫ d³r F × G = 0.

(c) Begin with the vector with components ∂_j (P_jG) and prove that

[dr = - [drrv. V V dr r(V. P) +dS(- P)r. S