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Unformatted text preview: blue MATH 32A Exam 1 January 30, 2008 LAST NAME FIRST NAME ID NO. Your TA: To receive credit, you must write your answer in the space provided . DO NOT WRITE BELOW THIS LINE 1 (20 pts) 5 (20 pts) 2 (10 pts) 6 (20 pts) 3 (20 pts) 7 (20 pts) 4 (20 pts) TOTAL 2 PROBLEM 1 (20 Points) (A) Determine  v 5 w  where the angle between v and w is θ = π 4 and their lengths are  v  = √ 2 ,  w  = 2 Answer : (B) Find cos θ where θ is the angle between vectors v and w such that  v  = 4 ,  w  = 3 ,  v + w  = 2 Answer : 3 Solution: (A) We have  v 5 w  2 = ( v 5 w ) · ( v 5 w ) = ( v · v ) 2( v · 5 w ) + (5 w ) · (5 w ) =  v  2 2(5)  v  w  cos π 4 + 25  w  2 = ( √ 2) 2 2(5)( √ 2)(2) √ 2 2 ! + 25(2 2 ) = 2 20 + 100 = 82 Thus  v 5 w  = √ 82. (B) We have 2 2 =  v + w  2 = ( v + w ) · ( v + w ) = ( v · v ) + 2( v · w ) + ( w · w ) =  v  2 + 2  v  w  cos θ +  w  2 = 4 2 + 2(4)(3) cos θ + 3 2 Therefore cos θ = 2 2 4 2 3 2 24 = 21 24 4...
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 Winter '08
 GANGliu
 Math, Conic section

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