M408D Quest Homework 7-solutions

M408D Quest Homework 7-solutions - hernandez (ah29758)...

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Unformatted text preview: hernandez (ah29758) M408D Quest Homework 7 pascaleff (54550) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find a unit vector n with the same direction as the vector v = 2 i + 3 j + 6 k . 1. n = 2 7 i 3 7 j 6 7 k 2. n = 2 7 i + 3 7 j + 6 7 k correct 3. n = 1 5 i + 3 10 j + 3 5 k 4. n = 2 9 i 1 3 j 2 3 k 5. n = 2 9 i + 1 3 j + 2 3 k 6. n = 1 5 i 3 10 j 3 5 k Explanation: The vector v = 2 i + 3 j + 6 k . has length | v | = radicalbig 2 2 + 3 2 + 6 2 = 49 = 7 . Consequently, n = v | v | = 2 7 i + 3 7 j + 6 7 k is a unit vector having the same direction as v . 002 10.0 points Determine the length of the vector 2 a + b when a = ( 1 , 3 , 2 ) , b = ( 3 , 1 , 3 ) . 1. length = 7 2. length = 51 correct 3. length = 47 4. length = 43 5. length = 3 5 Explanation: The length, | c | , of the vector c = ( c 1 , c 2 , c 3 ) is defined by | c | = radicalBig c 2 1 + c 2 2 + c 2 3 . Consequently, when a = ( 1 , 3 , 2 ) , b = ( 3 , 1 , 3 ) , and c = 2 a + b = ( 1 , 7 , 1 ) , we see that | 2 a + b | = 51 . 003 10.0 points Find all scalars so that ( a 2 b ) is a unit vector when a = ( 2 , 3 ) , b = ( 1 , 2 ) . 1. = 1 17 2. = 1 17 3. = 1 17 4. = 1 17 hernandez (ah29758) M408D Quest Homework 7 pascaleff (54550) 2 5. = 1 17 correct 6. = 1 17 Explanation: A vector c = ( c 1 , c 2 ) is said to be a unit vector when | c | = radicalBig c 2 1 + c 2 2 = 1 . But for the given vectors a and b , ( a 2 b ) = ( 4 , 1 ) = ( 4 , ) . Thus | ( a 2 b ) | = radicalBig 2 ((4) 2 + ( 1) 2 ) = | | radicalBig (4) 2 + ( 1) 2 = | | 17 . Consequently, ( a 2 b ) will be a unit vector if and only if = 1 17 . keywords: vector sum, length, linear combi- nation, unit vector, 004 10.0 points When u , v are the displacement vectors u = AB , v = AP , determined by the parallelogram A B C D P Q R S O express AS in terms of u and v . 1. AS = 2 v 2. AS = 2( u + v ) correct 3. AS = u + 2 v 4. AS = 2( u v ) 5. AS = 2 v u 6. AS = 2 u Explanation: By the parallelogram law for the addition of vectors we see that AS = 2( u + v ) . keywords: vectors, linear combination, vector sum displacement vector, parallelogram 005 10.0 points Find the vector v having a representation by the directed line segment AB with respect to points A (1 , 3 , 1) , B ( 4 , 2 , 2) . 1. v = ( 5 , 5 , 1 ) 2. v = ( 5 , 5 , 1 ) 3. v = ( 3 , 1 , 3 ) 4. v = ( 3 , 1 , 3 ) 5. v = ( 5 , 5 , 1 ) correct 6. v = ( 3 , 1 , 3 ) Explanation: Since AB = ( 4 1 , 2 + 3 , 2 + 1 ) , hernandez (ah29758) M408D Quest Homework 7 pascaleff (54550) 3 we see that...
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This note was uploaded on 11/15/2011 for the course M 408 D taught by Professor Textbookanswers during the Spring '07 term at University of Texas at Austin.

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M408D Quest Homework 7-solutions - hernandez (ah29758)...

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