# 09.14 - [Hand out time-sheets and group-work work-sheet and...

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[Hand out time-sheets and group-work work-sheet and true-false quiz questions on 92.142 material] [Collect true-false quizzes on 92.141 material] Paradox I asked you to think about for today: Let u be a vector such that | u |=1. Choose a vector v such that | v | = 3 and u v = 5. Now we have | u v | 2 = ( u v ) ( u v ) = u u – 2( u v ) + v v = 1 – 2(5) + 9 = 0. Hence u = v . But u and v have different lengths! What’s going on? ..?. . No such vectors exist! Why not? ..?. . Can we have | u | = 1, | v | = 3, and u v = 5? Why not? ..?. . By the Cauchy-Schwarz inequality, … ..?. . | u v | is less than or equal to | u | times | v |, but 5 is greater

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than 1 times 3. Section 10.4: The cross product a × b has magnitude equal to the area of the parallelogram spanned by a and b , which equals | a | | b | sin θ , where FIX THIS IN THE NOTES! (with 0 leq theta leq pi) is the angle between a and b , and a × b has direction perpendicular to both a and
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## This note was uploaded on 02/13/2012 for the course MATH 241 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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09.14 - [Hand out time-sheets and group-work work-sheet and...

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