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02spr-m1 - EXAM I Math 51 Spring 2002 You have 2 hours No...

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EXAM I Math 51, Spring 2002. You have 2 hours. No notes, no books, no calculators. YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING TO RECEIVE CREDIT Good luck! Name ID number 1. (/20 points) 2. (/30 points) 3. (/20 points) 4. (/10 points) 5. (/20 points) Bonus (/10 points) Total (/100 points) “On my honor, I have neither given nor received any aid on this examination. I have furthermore abided by all other aspects of the honor code with respect to this examination.” Signature: Circle your TA’s name: Tarn Adams (2 and 6) Mariel Saez (3 and 7) Yevgeniy Kovchegov (4 and 8) Heaseung Kwon (A02) Alex Meadows (A03) Circle your section meeting time: 11:00am 1:15pm 7pm 1
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1. Let -→ u = 0 3 1 -→ v = 3 2 2 -→ w = 2 3 4 (a) Compute the length of each of the given vectors, and the dot product for each pair. (b) Let θ -→ u , -→ v be the angle formed at the origin between the vectors -→ u and -→ v . Evaluate cos( θ -→ u , -→ v ) 2
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(c) Find a linear dependence of the three vectors given, or prove that they are indepen- dent.
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