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Unformatted text preview: qazi (kaq87) HW04 berg (55290) 1 This printout should have 11 questions. Multiplechoice 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. 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 welldefined because it is the product of a scalar and a vector. II. is not welldefined because the first term in the dot product is not a vector. III. is welldefined because both terms in the dot product are vectors. keywords: vectors, dot product, T/F, length, TrueFalse, 002 10.0 points 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 10.0 points 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 ....
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This note was uploaded on 03/28/2012 for the course M 408 M taught by Professor Gilbert during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Gilbert
 Multivariable Calculus, Vectors

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