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Unformatted text preview: moseley (cmm3869) HW09 Gilbert (56380) 1 This printout should have 23 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine the dot product of the vectors a = i + 2 j + k , b = i 3 j + k . 1. a b = 4 correct 2. a b = 10 3. a b = 2 4. a b = 6 5. a b = 8 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 + 2 j + k , b = i 3 j + k , we see that a b = 4 . 002 10.0 points Determine the dot product of vectors a , b when  a  = 5 ,  b  = 3 and the angle between a and b is / 3. 1. a b = 8 2. a b = 7 3. a b = 9 4. a b = 15 2 correct 5. a b = 17 2 Explanation: The dot product of vectors a , b is defined in coordinatefree form by a b =  a  b  cos where is the angle between a and b . For the given vectors, therefore, a b = 15 cos 3 = 15 2 . 003 10.0 points Which of the following statements are true for all vectors a , b ? A.  a b  2 =  a  2 + 2 a b +  b  2 , B.  a b  =  a  b  = a bardbl b , C. a b = 0 = a = 0 or b = 0. 1. A only 2. C only 3. A and B only 4. A and C only 5. B and C only 6. none of them 7. all of them 8. B only correct Explanation: If is the angle between a and b , then a b =  a  b  cos . moseley (cmm3869) HW09 Gilbert (56380) 2 A. FALSE: since  a  2 = a a ,  a b  2 = ( a b ) ( a b ) =  a  2 a b b a +  b  2 =  a  2 2 a b +  b  2 because a b = b a . B. TRUE: since  a b  =  a  b  =  cos  = 1 , it follows that = 0 or , in which case a bardbl b . C. FALSE: if a b , then = / 2. But then cos = 0. So a b = 0 when a b , as well as when a = 0 or b = 0. keywords: 004 10.0 points Find the angle between the vectors a = ( 2 3 , 1 ) , b = ( 3 3 , 5 ) . 1. angle = 2 3 2. angle = 3 4 3. angle = 3 correct 4. angle = 6 5. angle = 5 6 6. angle = 4 Explanation: Since the dot product of vectors a and b can be written as a . b =  a  b  cos , , where is the angle between the vectors, we see that cos = a . b  a  b  , . But for the given vectors, a b = (2 3)(3 3) + ( 1)(5) = 13 , while  a  = 13 ,  b  = 52 . Consequently, cos = 13 13 2 13 = 1 2 where 0 . Thus angle = 3 . 005 10.0 points For which positive value of x are the vectors ( 24 x, 2 , 1 ) , ( 2 , 5 x 2 , 10 ) orthogonal?...
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 Spring '07
 Sadler
 Multivariable Calculus, Vectors, Dot Product

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