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# hmwk1 - 13.2b Suppose a =-1 1 2 and b = 2-1-1 Sketch each...

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Math 215 Homework Set 1: §§ 13.1 – 13.4 Winter 2008 Most of the following problems are modified versions of 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 4 x - 2 y + z - 4 = 0 . 13.1c. Find an equation for the set of all points equidistant from the points S = (2 , 1 , 3) and T = ( - 2 , - 2 , - 2) . Describe the set. 13.1d. Describe, in words, the region in R 3 represented by the inequality x 2 + y 2 - 16 0 . 13.2a. Molly Brown is walking due north on the deck of the Titanic at a speed of 3 km/hr. The Titanic is moving due west at a speed of 30 km/hr. Find Molly’s velocity relative to the surface of the water.
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Unformatted text preview: 13.2b. Suppose a = -1 , 1 , 2 and b = 2 ,-1 ,-1 . Sketch each of the following quantities. (a) a + 4 j (b) 2 a-3 b 13.3a. Suppose u and v are vectors. We dene 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 and v = 1 , 5 , 8 . 13.3b. Compute the three angles, correct to the nearest tenth of a radian, of the triangle with vertices (1 , 2 , 3) , (3 , 5 ,-1) , and (-2 ,-3 ,-4) . List your answers from least to greatest. 13.4b. Suppose a = -1 , 3 ,-2 and b = 2 ,-1 ,-1 . Compute a b . Sketch a , b , and a b . 13.4c. Find two unit vectors orthogonal to 1 , 2 , 4 . Can you nd others? 1 For example, you may wish to do a bit of research in a library....
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