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Gilbert_Hmwk08sol

# Gilbert_Hmwk08sol - moseley(cmm3869 – HW08 – Gilbert...

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Unformatted text preview: moseley (cmm3869) – HW08 – Gilbert – (56380) 1 This print-out should have 15 questions. Multiple-choice 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 3-space? 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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Gilbert_Hmwk08sol - moseley(cmm3869 – HW08 – Gilbert...

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