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Unformatted text preview: blue MATH 32A Exam 1 October 23, 2007 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 (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 2 PROBLEM 1 (40 Points) Let v = ( 1 , 2 , 1 ) , w = ( 1 , 1 , 1 ) Let be the angle between v and w . Calculate the quantities (A)(D). (A) v w = . (B) cos = . (C) v w = . (D) The volume of the parallelepiped spanned by the vec tors k , v and w . Volume = Solution: v w = 1(1) + 2( 1) + ( 1)(1) = 2 . cos = v w  v   w  = 2 radicalbig 1 + 2 2 + ( 1) 2 radicalbig 1 2 + ( 1) 2 + 1 2 = 2 6 3 = 2 3 2 = 2 3 v w = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle i j k 1 2 1 1 1 1 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = i 2 j 3 k = ( 1 , 2 , 3 ) Volume of the parallelepiped spanned by the vectors...
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This test prep was uploaded on 04/22/2008 for the course MATH 32A taught by Professor Gangliu during the Winter '08 term at UCLA.
 Winter '08
 GANGliu
 Math

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