m1sol-20C-su2004

m1sol-20C-su2004 - Name: Math 20C. Midterm Exam 1 July 9,...

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Name: Student Number: Math 20C. Midterm Exam 1 July 9, 2004 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. (4 points) Consider the vectors ~v = 2 ~ i - 2 ~ j + ~ k and ~w = ~ i + 2 ~ j - ~ k . (a) Compute ~v · ~w . ~v · ~w = h 2 , - 2 , 1 i · h 1 , 2 , - 1 i = 2 - 4 - 1 = - 3 . (b) What is the cosine of the angle between ~v and ~w ? | ~v | = 4 + 4 + 1 = 3 , | ~w | = 1 + 4 + 1 = 6 . cos( θ ) = ~v · ~w | ~v || ~w | = - 3 3 6 = - 1 6 . (c) Find a unit vector in the direction of ~v . ~u = ~v | ~v | = 1 3 h 2 , - 2 , 1 i . # Score 1 2 3 4 Σ
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2. (4 points) Find the equation of the plane that contains the lines ~ r 1 ( t ) = h 1 , 2 , 3 i t and ~ r 2 ( t ) = h 1 , 1 , 0 i + h 1 , 2 , 3 i t . P 0 = (1 , 1 , 0) is in the plane. P 1 = (1 , 2 , 3) = ~ r 1 ( t = 1) is also in the plane. Therefore,
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This note was uploaded on 04/30/2008 for the course MATH 20C taught by Professor Helton during the Summer '08 term at UCSD.

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m1sol-20C-su2004 - Name: Math 20C. Midterm Exam 1 July 9,...

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