Chapter 16.5, Problem 27E

Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f is a scalar field and F, G are vector fields, then fF, F · G, and F × G are defined by

(fF)(x, y, z) = f(x, y, z) F(x, y, z)

(F · G)(x, y, z) = F(x, y, z) · G(x, y, z)

(F × G)(x, y, z) = F(x, y, z) × G(x, y, z)

27. div(F × G) = G · curl F − F · curl G