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15----blueexam1sol[1] - blue MATH 32A Exam 1 LASTNAME FIRST...

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Sheet1 Page 1 blue MATH 32A Exam 1 October 23, 2007 LASTNAME FIRST NAME IDNO. YourTA: To receive credit, you must write your answer in the space provided. DO NOT WRITE BELOW THIS LINE 1 (40 pts) 6 (20 pts) 2 (10 pts) 7 (20 pts) 3 (20 pts) 8 (30 pts) 4 (20 pts) 9 (20 pts) 5 (20 pts) TOTAL
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Sheet1 Page 2 PROBLEM 1 (40 Points) Let v Err:509 Err:509 Let be the angle between v and w. Calculate the quantities(A)-(D). (A) v Err:520 . (B) cos = . (C) v w Err:520 . (D)The volume of the parallelepiped spanned by the vect ors k, v and w. Volume = Solution: v Err:509 v -2 cos == +(-1)2 12 +(-1)2 12 v h w h w h w pp ||v||h||w|| 1+22
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Sheet1 Page 3 -2 -2 - 2 Err:520 633 2 3 ij k v w #NAME? -2j -3k Err:509 1 -11 Volume of the parallelepiped spanned by the vectors k, v and w is |k w|= |-3|=3 PROBLEM 2 (10 Points) Is the z-component of the cross product w v positive or negative? z wvx x y Answer : h (v
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Sheet1 Page 4 Solution: positive p PROBLEM 3 (20 Points) Find parametric equations of the line through the point P0 Err:509 Err:509 Answer : Solution: The vectorparametrizationis r(t)= h4,3,-2i+ th1,1,-1i = h4+t,3+t,-2-ti
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