problem3_pdf - huang(jwh2377 Homework 3 Kushner(56640 This...

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huang (jwh2377) – Homework 3 – Kushner – (56640) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Which of the following expressions are well- defined for all vectors a , b , and c ? I. ( a · b ) · c , II. a · ( b + c ) , III. | a | · ( b · c ) . 1. II and III only 2. none of them 3. I only 4. II only 5. I and III only 6. all of them 7. III only 8. I and II only 002 10.0 points Find the angle between the vectors a = ( 3 , 2 ) , b = ( − 5 , 3 ) . 1. angle = 5 π 6 2. angle = π 3 3. angle = π 4 4. angle = 3 π 4 5. angle = π 6 6. angle = 2 π 3 003 10.0 points Determine the dot product of vectors a , b when | a | = 1 , | b | = 4 and the angle between a and b is π/ 3. 1. a · b = 3 2. a · b = 3 2 3. a · b = 2 4. a · b = 5 2 5. a · b = 7 2 004 10.0 points Find the scalar projection of b onto a when b = 3 i + 3 j + 2 k , a = i 2 j 2 k . 1. scalar projection = 7 3 2. scalar projection = 1 3. scalar projection = 2 4. scalar projection = 4 3 5. scalar projection = 5 3 005 10.0 points Find the vector projection of b onto a when b = ( 4 , 1 ) , a = ( 3 , 2 ) . 1. vector proj. = 14 13 ( 4 , 1 ) 2. vector proj. = 14 13 ( 3 , 2 )
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huang (jwh2377) – Homework 3 – Kushner – (56640) 2 3. vector proj. = 14 13 ( 4 , 1 ) 4. vector proj. = 16 13 ( 3 , 2 ) 5. vector proj. = 16 13 ( 3 , 2 ) 6. vector proj. = 16 13 ( 4
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