This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Gauthier, Joseph Homework 5 Due: Sep 29 2007, 3:00 am Inst: JEGilbert 1 This printout should have 26 questions. Multiplechoice 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 3space? 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 ....
View
Full
Document
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.
 Fall '07
 Gilbert

Click to edit the document details