HW_5_Key - Miller, Kierste – Homework 5 – Due: Sep 29...

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Unformatted text preview: 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 , 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 ....
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This note was uploaded on 05/08/2008 for the course M 408 M taught by Professor Gilbert during the Fall '07 term at University of Texas.

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HW_5_Key - Miller, Kierste – Homework 5 – Due: Sep 29...

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