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HW_5_Key - Miller Kierste Homework 5 Due 3:00 am Inst...

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Miller, Kierste – 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. - --→ QP , B. --→ PQ , are representations of vectors when P, Q are points in 3-space? 1. A only 2. both of them correct 3. B only 4. neither of them Explanation: A. TRUE: - --→ QP is the displacement vector having initial point P and terminal point Q . 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 (5 , - 1) and B (4 , 4). 1. v = h- 9 , 3 i 2. v = h 1 , 5 i 3. v = h 9 , 3 i 4. v = h 9 , - 3 i 5. v = h- 1 , 5 i correct 6. v = h- 1 , - 5 i Explanation: Since --→ AB = h 4 - 5 , 4 + 1 i , we see that v = h- 1 , 5 i . keywords: vectors, directed line segment, 003 (part 1 of 1) 10 points Determine the vector c = a + 2 b when a = - 2 i + 3 j + 2 k , b = 2 i + j + 2 k . 1. c = 2 i + 5 j - 5 k 2. c = 2 i - 6 j + 6 k 3. c = 3 i + 5 j - 5 k 4. c = 3 i - 6 j + 6 k 5. c = 2 i + 5 j + 6 k correct 6. c = 3 i - 6 j - 5 k 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 λ also is defined componentwise: λ a = ( λa 1 ) i + ( λa 2 ) j + ( λa 3 ) k . When a = - 2 i + 3 j - 2 k , b = 2 i - j + 2 k ,
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Miller, Kierste – Homework 5 – Due: Sep 29 2007, 3:00 am – Inst: JEGilbert 2 therefore, we see that c = (1)( - 2) + (2)(2) · i + (1)(3) + (2)(1) · j + (1)(2) + (2)(2) · k . Consequently, c = 2 i + 5 j + 6 k . keywords: vectors, vector sum, linear combi- nation 004 (part 1 of 1) 10 points Determine the length of the vector a - 2 b when a = h 3 , 2 , - 1 i , b = h - 2 , 2 , - 1 i . 1. length = 3 6 correct 2. length = 2 13 3. length = 58 4. length = 5 2 5. length = 2 14 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 3 , 2 , - 1 i , b = h - 2 , 2 , - 1 i , and c = a - 2 b = h 7 , - 2 , 1 i , we see that | a - 2 b | = 3 6 . 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 + 3 j + 2 k . 1. n = 3 5 i - 3 10 j - 1 5 k 2. n = 6 7 i - 3 7 j - 2 7 k 3. n = 3 5 i + 3 10 j + 1 5 k 4. n = 6 7 i + 3 7 j + 2 7 k correct 5. n = 2 3 i - 1 3 j - 2 9 k 6. n = 2 3 i + 1 3 j + 2 9 k Explanation: The vector v = 6 i + 3 j + 2 k . has length | v | = p 6 2 + 3 2 + 2 2 = 49 = 7 . Consequently, n = v | v | = 6 7 i + 3 7 j + 2 7 k is a unit vector having the same direction as v . keywords: vector, length, unit vector,
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Miller, Kierste – Homework 5 – Due: Sep 29 2007, 3:00 am – Inst: JEGilbert 3 006 (part 1 of 1) 10 points Leonardo walks due north on the deck of the Titanic at 3 miles per hour, while the ship is moving west at a speed of 10 miles per hour.
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