OldExam7 - MATH 2008/09B WINTER 2008 AN OLD FINAL EXAM 1....

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MATH 2008/09B WINTER 2008 AN OLD FINAL EXAM 1. Find the distance between the skew lines L 1 : x = 2 t, y = 3 + 4 t, z = 2 t and L 2 : x = 1 + t, y = 2 , z = 1 + 2 t . ( Hint: (a) Find the equation of the plane π passing through the line L 2 and parallel to the line L 1 . (b) Find the distance from the line L 1 to the plane π .) 2. Find parametric equations of the line through the point (1 , 2 , 3) that is perpendic- ular to both the x -axis and the line x 4 2 = y 3 1 = z 5 . 3. A particle has the velocity V ( t ) = (1 , 2 t, t 2 ). Let the initial position vector be r (0) = (0 , 0 , 0); (a) Find the position function of the motion; (b) Find the unit tangent vector at the point p 1 , 1 , 1 3 P ; (c) Find the tangential and normal components of the acceleration vector at the point p 1 , 1 , 1 3 P ; (d) Find the unit normal and binormal vectors at the point p 1 , 1 , 1 3 P ; (e) Find the curvature at the point p 1 , 1 , 1 3 P ; (f) Find the radius of the osculating circle at the point
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This note was uploaded on 05/26/2010 for the course MATH Math2008 taught by Professor Monadi during the Fall '08 term at Carleton.

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OldExam7 - MATH 2008/09B WINTER 2008 AN OLD FINAL EXAM 1....

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