MATH 2163 Quiz: MATH 2163 OK State Quiz2
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Quiz # 1 math 2163, calculus iii aug 24, 2007. Show all your work neatly and concisely, and indicate your nal answer clearly: given two vectors a =< 1, 2, 2 > and b =< 3, 3, 4 >, nd projab. Let be the angle between a and b. Then by the equation a b = |a||b| cos , we have a b. |a||b| cos = ( 1)(3) + ( 2)(3) + (2)(4) p( 1)2 + ( 2)2 + (2)2p(3)2 + (3)2 + (4)2. Next, we solve the problem in two steps: (a) the length of projab, which is usually denoted by compab, is compab = |b| cos = 34 1. 3 (b) the direction of projab is decided by the unit vector a. Put together the length and the direction, we have projab = . Remark 1: if you remember the formula projab = a b directly that. |a|2 a, you can use it to calculate projab = 1.
