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HW04-solutions

# HW04-solutions - qazi(kaq87 HW04 berg(55290 This print-out...

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qazi (kaq87) – HW04 – berg – (55290) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points 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. I only 2. none of them 3. II and III only 4. II only 5. all of them 6. III only 7. I and II only 8. I and III only correct Explanation: The dot product is defined only for two vectors, and its value is a scalar. On the other hand, the length of any vector is always a scalar. For the three given expressions, therefore, we see that I. is well-defined because it is the product of a scalar and a vector. II. is not well-defined because the first term in the dot product is not a vector. III. is well-defined because both terms in the dot product are vectors. keywords: vectors, dot product, T/F, length, TrueFalse, 002 10.0points Determine the dot product of the vectors a = i 3 j + 2 k , b = 2 i j 2 k . 1. a · b = 5 2. a · b = 3 3. a · b = 1 correct 4. a · b = 1 5. a · b = 3 Explanation: The dot product, a · b , of vectors a = a 1 i + a 2 j + a 3 k , b = b 1 i + b 2 j + b 3 k is defined by a · b = a 1 b 1 + a 2 b 2 + a 3 b 3 . Consequently, when a = i 3 j + 2 k , b = 2 i j 2 k , we see that a · b = 1 . 003 10.0points Which of the following statements are true for all vectors a , b ? A. | a · b | ≤ | a | | b | , B. | a + b | 2 = | a | 2 + 2 a · b + | b | 2 , C. | a · b | = | a || b | = a b . 1. B and C only 2. A and B only correct 3. A and C only 4. B only

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qazi (kaq87) – HW04 – berg – (55290) 2 5. all of them 6. none of them 7. A only 8. C only Explanation: If θ
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HW04-solutions - qazi(kaq87 HW04 berg(55290 This print-out...

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