2.31 Let A and B be vector functions of position vector x with continuous first and second derivatives, and let F and G be scalar functions of position x with continuous first and second derivatives. Show that: (a) V. (V x A) = 0. (b) ▼x (VF) = 0. (c) V (VF x VG) = 0. (d) V. (FA) = A·VF+ FV.A.

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