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Unformatted text preview: Name : PID : TA : Sec. No : Sec. Time : Math10C Final Exam. December 9 2010 Turn off and put away your cell phone. No calculators or any other electronic devices are allowed during this exam. You may use one page of notes, but no books or other assistance during the exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write all your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. # Points Score 1 6 2 6 3 8 4 6 5 6 6 6 7 8 8 8 Σ 54 Problem 1 (6 points): Let ~a = ~ i + 3 ~ j + 2 ~ k, ~ b = 2 ~ i ~ j + ~ k. (a) Find the lengths of ~a and ~ b . Solution:  ~a  = √ 1 + 9 + 4 = √ 14 1 point  ~ b  = √ 4 + 1 + 1 = √ 6 1 point (b) Find the angle between ~a and ~ b . Solution: ~a · ~ b = 2 3 + 2 = 3 1 point θ = cos 1 3 √ 14 √ 6 1 point (c) Find a unit vector perpendicular to both ~a and ~ b . Solution: ~a × ~ b = (5 , 5 , 5) 1 point so a unit vector perpendicular to both ~a and ~ b is ~a × ~ b  ~a × ~ b  = 1 √ 75 (5 , 5 , 5) = 1 √ 3 (1 , 1 , 1) . 1 point Problem 2 (6 points): If z = x 3 xy 2 y 4 , x = 3 cos 2 t u , and y = 2 e t sin u , find ∂z ∂t and ∂z ∂u ....
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This note was uploaded on 03/28/2011 for the course MATH 20C taught by Professor Helton during the Winter '08 term at UCSD.
 Winter '08
 Helton
 Math

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