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homework02_w12 - Math 215 Homework Set 2 12.413.2 Winter...

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Math 215 Homework Set 2: §§ 12.4–13.2 Winter 2012 Most of the following problems are modified versions of the problems from your text book, Multivariable Calculus , 7th ed., by James Stewart. Your solution to each problem should be complete, show all work, and be written in complete sentences where appropriate. For Maple problems, include a print-out that shows all of the work and graphs that you generated in Maple to solve the problem, in addition to any work you may have done by hand. 12.4.1: Let a be a vector whose z -component is zero, and whose x - and y -components are both positive, such that | a | = 3 . Let b be a vector in the direction of k such that | b | = 4 . Sketch a and b with initial point at the origin in the 3 dimensional Cartesian coordinate system. (a) Find | a × b | . (b) Use the right hand rule to determine whether the components of a × b are positive, negative, or zero. 12.4.2: Find two unit vectors orthogonal to both 2 i + 2 j - k and - j + k . Are there any others? Explain.
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