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blueexam1sol.08w

# blueexam1sol.08w - blue MATH 32A Exam 1 LAST NAME FIRST...

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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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blueexam1sol.08w - blue MATH 32A Exam 1 LAST NAME FIRST...

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