MTH164FA10-M1d_ans

20 points suppose xt et y t 2 sin2t and z t

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Unformatted text preview: = ￿1, 1, 1, 0￿. Write u v ￿ = w1 + w2 v￿ ￿ where w1 is parallel to ￿ and w2 is perpendicular to ￿ . ￿ u ￿ u Answer: There are several approaches. One is to use vector projection onto ￿ to calculate w1 , then u ￿ subtract to find w2 . Another is to use w1 = k￿ , ￿ · w2 = 0. Solving the equation above for w2 ￿ ￿ uu￿ ￿ and using these two equations we have ￿ · (￿ − k￿ . Since only k is unknown in this equation uv u we can solve for k and the rest follows. Answer: w1 = ￿ 1 , 0, 1, 1 ￿ and w2 = ￿ 1 , 1, 0, − 1 ￿ ￿ ￿ 2 2 2 2 5. (20 points) Suppose x(t) = et , y (t) = 2 + sin(2t) and z (t) = 2 + cos(4t). If w(x, y, z ) = evaluate xy + yz dw when t = 0. dt...
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This document was uploaded on 05/06/2013.

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