Math 215Homework Set 2:§§12.4–13.2Winter 2012Most of the following problems are modified versions of the problems from your text book,MultivariableCalculus, 7th ed., by James Stewart. Your solution to each problem should be complete, show all work,and be written in complete sentences where appropriate. ForMapleproblems, include a print-out thatshows all of the work and graphs that you generated inMapleto solve the problem, in addition to anywork you may have done by hand.12.4.1: Letabe a vector whosez-component is zero, and whosex- andy-components are both positive,such that|a|= 3. Letbbe a vector in the direction ofksuch that|b|= 4. Sketchaandbwithinitial 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 ofa×bare positive, negative,or zero.12.4.2: Find two unit vectors orthogonal to both2i+ 2j-kand-j+k. Are there any others? Explain.
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