hmwk1 - moving due west at a speed of 40 km/hr Find...

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Math 215 Homework Set 1: §§ 13.1 – 13.3 Fall 2007 Most of the following problems are modified versions of the recommended homework problems from your text book Multivariable Calculus by James Stewart. 13.1a. Prove the Pythagorean theorem. (Hint: We do not expect you to produce an original proof. Rather, we expect you to find 1 a solution, understand the solution, and reproduce the solution. Please properly acknowledge all references you use. Also note that a proof which uses sin or cos probably is not a proof. Also, handing in a copy of something you find in cyberspace is not acceptable.) 13.1b. Sketch the surface in R 3 represented by the equation 3 x - 2 y + 2 z + 12 = 0 . 13.1c. Find an equation for the set of all points equidistant from the points S = (1 , 2 , 3) and T = ( - 3 , - 3 , - 3) . Describe the set. 13.1d. Describe, in words, the region in R 3 represented by the inequality 4 x 2 + 4 y 2 - 25 0 . 13.2a. Jack Dawson is walking due north on the deck of the Titanic at a speed of 3 km/hr. The Titanic is
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Unformatted text preview: moving due west at a speed of 40 km/hr. Find Jack’s velocity relative to the surface of the water. 13.2b. Suppose a = ±-2 , 3 ,-2 ² and b = ± 3 , 4 ,-1 ² . Sketch each of the following quantities. (a) a + 5 j (b) 3 a-4 b 13.3a. Suppose u and v are vectors. We define orth u v to be the difference v-proj u v . (a) Show that v = proj u v + orth u v . (b) Show that proj u v is orthogonal to orth u v . (c) Compute and sketch the vectors proj u v and orth u v for u = ± 2 , 5 , 7 ² and v = ± 1 , 5 , 8 ² . 13.3b. Compute the three angles, correct to the nearest tenth of a radian, of the triangle with vertices (2 , 2 , 3) , (2 ,-5 , 1) , and (1 ,-3 , 4) . List your answers from least to greatest. 1 For example, you may wish to do a bit of research in a library....
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