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Unformatted text preview: Math 20E, Midterm 1 Solutions April 25, 2007 Name : PID : TA : Sec. No : Sec. Time : This exam consists of 6 pages including this front page. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justification will receive no credit. 3. You may use one 4by6 index card, both sides. 4. Show your ID on your desk. Score 1 10 2 10 3 10 4 10 5 10 Total 50 1 1. (a) Give a unit vector that points in the same direction as the vector 2 i j + k . Answer :  2 i j + k  = p 2 2 + ( 1) 2 + 1 2 = √ 6 . Hence the unit vector is 1 √ 6 (2 i j + k ) = 2 √ 6 i 1 √ 6 j + 1 √ 6 k . (b) Give a parametric equation of the line in R 3 going though the point (1 , 4 , 5) and (2 , 4 , 1). Answer : As a direction vector, we can choose (2 , 4 , 1) (1 , 4 , 5) = (1 , , 6) . Hence a parametric equation is ( x, y, z ) = (1 , 4 , 5) + t (1 , , 6) ....
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 Spring '07
 Enright
 Math, Derivative, Vector Calculus, Vector Space, Cartesian Coordinate System, Polar coordinate system, Taylor Polynomial

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