HW5S - Gauthier, Joseph Homework 5 Due: Sep 29 2007, 3:00...

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Unformatted text preview: Gauthier, Joseph Homework 5 Due: Sep 29 2007, 3:00 am Inst: JEGilbert 1 This print-out should have 26 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Which, if any, of the following A. | PQ | , B.-- PQ, are representations of vectors when P, Q are points in 3-space? 1. both of them 2. A only 3. B only correct 4. neither of them Explanation: A. FALSE: | PQ | is the length of the line segment PQ . B. TRUE:-- PQ is the displacement vector having initial point P and terminal point Q . keywords: vectors, scalars, T/F, line segment, displacement vector, length 002 (part 1 of 1) 10 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 = h 3 , 2 i 2. v = h- 5 , 8 i 3. v = h- 3 , 2 i 4. v = h 5 , 8 i correct 5. v = h 3 ,- 2 i 6. v = h 5 ,- 8 i Explanation: Since-- AB = h 4 + 1 , 5 + 3 i , we see that v = h 5 , 8 i . keywords: vectors, directed line segment, 003 (part 1 of 1) 10 points Determine the vector c =- a- 2 b when a =- 3 i + j + 3 k , b =- 2 i + 2 j + 3 k . 1. c = 6 i- 5 j + 10 k 2. c = 7 i + 4 j- 9 k 3. c = 6 i + 4 j + 10 k 4. c = 6 i + 4 j- 9 k 5. c = 7 i- 5 j + 10 k 6. c = 7 i- 5 j- 9 k correct Explanation: The sum of vectors a = a 1 i + a 2 j + a 3 k , b = b 1 i + b 2 j + b 3 k is defined componentwise: a + b = ( a 1 + b 1 ) i + ( a 2 + b 2 ) j + ( a 3 + b 3 ) k ; similarly, multiplication by a scalar also is defined componentwise: a = ( a 1 ) i + ( a 2 ) j + ( a 3 ) k . When a =- 3 i + j- 3 k , b =- 2 i- 2 j + 3 k , Gauthier, Joseph Homework 5 Due: Sep 29 2007, 3:00 am Inst: JEGilbert 2 therefore, we see that c = (- 1)(- 3)- (2)(- 2) i + (- 1)(1)- (2)(2) j + (- 1)(3)- (2)(3) k . Consequently, c = 7 i- 5 j- 9 k . keywords: vectors, vector sum, linear combi- nation 004 (part 1 of 1) 10 points Determine the length of the vector- 2 a- b when a = h- 1 ,- 2 , 2 i , b = h 3 , 2 ,- 1 i . 1. length = 2 2 2. length = 10 3. length = 2 3 4. length = 14 correct 5. length = 6 Explanation: The length, | c | , of the vector c = h c 1 ,c 2 ,c 3 i is defined by | c | = q c 2 1 + c 2 2 + c 2 3 . Consequently, when a = h- 1 ,- 2 , 2 i , b = h 3 , 2 ,- 1 i , and c =- 2 a- b = h- 1 , 2 ,- 3 i , we see that |- 2 a- b | = 14 . keywords: vectors, vector sum, length, linear combination 005 (part 1 of 1) 10 points Find a unit vector n with the same direction as the vector v = 6 i- 2 j- 3 k . 1. n = 3 5 i- 1 5 j- 3 10 k 2. n = 2 3 i + 2 9 j + 1 3 k 3. n = 6 7 i + 2 7 j + 3 7 k 4. n = 6 7 i- 2 7 j- 3 7 k correct 5. n = 2 3 i- 2 9 j- 1 3 k 6. n = 3 5 i + 1 5 j + 3 10 k Explanation: The vector v = 6 i- 2 j- 3 k ....
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This homework help was uploaded on 03/19/2008 for the course M 408M taught by Professor Gilbert during the Fall '07 term at University of Texas at Austin.

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HW5S - Gauthier, Joseph Homework 5 Due: Sep 29 2007, 3:00...

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