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Unformatted text preview: MA/PH 607 10/14/2011 Howell TAKE HOME PORTION OF TEST II (40 points) GENERAL NOTES: Due at the beginning of class on Friday, October 21. This is NOT to be a team effort. Do your own work! (You may, of course, consult with the instructor.) Hand in the next two pages containing your final answers along with additional sheets showing how you got your answers (I will be looking at your work as clearly well as your final answers!) Do use decimal approximations. ! Besides, using decimal not # "%"%#" approximations will just make the arithematic harder in these problems. For the most part, you might as well do the calculations by hand, especially since I do not want to see any decimal approximations. However, at one point you may have to multiply three matrices together. You can use a computer math $$ system (Maple, Mathematica, etc.) for this. Just include a printout of your program for the computation. (And remember, no decimal approximations.) You can simplify life by remembering a little algebra, such as illustrated here: " " & & " # #! & " # " & " & & # MA/PH 607 Take Home Portion of Test II NAME: I . The following concerns vectors in a traditional, threedimensional vector space. For these problems, assume T e f i j k is a standard basis (i.e., is orthonormal and right-handed), and let and be, respectively, T 9 a the vector and angle 1 a i j k &# " # and . 9 1 ' 1. Find a right-handed, orthonormal basis such that points in the U e f b b b b " # $ $ same direction as . The s should be expressed in terms of , and (as was , a b i j k a 5 above). Be sure to convince me that is both orthnormal and right-handed in your work....
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- Summer '11