(For masochists only.) Prove product rules (ii) and (vi).

QUESTION:

(For masochists only.) Prove product rules (ii) and (vi). Refer to Prob. 1.22 for the definition of

(A · )B.

Reference: (ii) and (vi).

Reference: Prob. 1.22:

(a) If A and B are two vector functions, what does the expression (A · )B mean?

(That is, what are its x, y, and z components, in terms of the Cartesian components

of A, B, and ?)

(b) Compute ( · ), where  is the unit vector defined in Eq. 1.21.

(c) For the functions in Prob. 1.15, evaluate (va · )vb.

Reference: Eq. 1.21:

Prove product rules (i), (iv), and (v).