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The solutions to homework problem 5 in vector calculus. It includes the calculations for parts (a) to (f) of problem 70. The document also explains the product rule and its application to the cross product.
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Solutions homework 5.
Problem page 70: 1. Solution: (a) F′(t) = cos ti − sin tj. (b) F′(t) · k = 0. (c) F′(t) · j = − sin t = 0 for t = nπ where n = 0, ± 1 , ± 2 , · · ·.
(d) Yes, since |F(t)| =
sin^2 t + cos^2 t + 1 =
(e) Yes, since |F′(t)| =
cos^2 t + sin^2 t = 1. (f) F′′(t) = − sin ti − cos tj. Problem page 70: 2. Solution: See back of the book. Problem page 70: 4. Note for any vector A, we have A × A = 0. Now by the product rule d dt
dR dt
dR dt
dR dt
d^2 R dt^2
d^2 R dt^2
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