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Unformatted text preview: moseley (cmm3869) HW08 Gilbert (56380) 1 This printout should have 15 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Which, if any, of the following A.  PQ  , B. PQ, are representations of vectors when P, Q are points in 3space? 1. A only 2. both of them 3. neither of them correct 4. B only Explanation: A. FALSE:  PQ  is the length of the line segment PQ . B. FALSE: PQ is the line segment from P to Q . keywords: vectors, scalars, T/F, line segment, displacement vector, length 002 10.0 points Find the vector v having a representation by the directed line segment AB with respect to points A (1 , 3) and B (4 , 5). 1. v = ( 5 , 2 ) 2. v = ( 3 , 8 ) correct 3. v = ( 3 , 8 ) 4. v = ( 3 , 8 ) 5. v = ( 5 , 2 ) 6. v = ( 5 , 2 ) Explanation: Since AB = ( 4 1 , 5 + 3 ) , we see that v = ( 3 , 8 ) . 003 10.0 points When u , v are the displacement vectors u = AP , v = AC , determined by the parallelogram A B C P Q R S O express QP in terms of u and v . 1. QP = 1 2 u v 2. QP = 1 2 v u 3. QP = u + 1 2 v 4. QP = 1 2 u 5. QP = 1 2 v correct 6. QP = 1 2 u + v Explanation: By the parallelogram law for the addition of vectors we see that QP = 1 2 v . moseley (cmm3869) HW08 Gilbert (56380) 2 004 10.0 points Determine a so that the vector u = ( 12 , 9 ) is a linear combination u = a v + b w of vectors v = ( 2 , 2 ) , w = ( 2 , 1 ) . 1. a = 3 correct 2. a = 2 3. a = 3 4. a = 1 5. a = 1 Explanation: Since addition and scalar multiplication of vectors is carried out componentwise, we see that u = ( 12 , 9 ) = a ( 2 , 2 ) + b ( 2 , 1 ) = ( 2 a 2 b, 2 a + b ) . Thus 2 a 2 b = 12 , 2 a + b = 9 . Consequently, after solving these for a we see that a = 3 . keywords: vectors, vector sum, linear combi nation 005 10.0 points Use vectors in the plane to determine the coordinates of the vertex S of the parallelo gram shown in P Q R S having vertices P (5 , 2) , Q (10 , 4) , R (12 , 8) ....
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This note was uploaded on 04/12/2011 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Sadler
 Multivariable Calculus

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