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Unformatted text preview: 18.02a Practice Midterm Questions, Fall 2009 Problems 15 cover material from the first unit. This will be on the midterm, but won’t be emphasized. Problems 15 take about 11.5 hours, problems 617 take 23 hours. The actual test will be shorter –designed to take 2 hours, with simpler arithmetic. Problem 1. Consider the point P = (20 , , 0), the plane P : x + 2 y + 3 z = 6 , and the point Q = (1 , 1 , 1) on P . a) Compute the distance from P to P . b) Give parametric equations for the line through P and perpendicular to P . c) Find the point of intersection between P and the line of part(b). For later reference, call this point R. d) Find the angle, ∠ PQR. e) By computing  PR  directly, verify your answer to part (a). f) Find the area of the triangle with vertices P, Q and R. Problem 2. Suppose tape is unwound from a roll in such a way that it is always vertical. Assuming the roll is centered at the origin and has radius 2, and the end of the tape starts at the point (2 , 0), give parametric equations for the path traced out by the end of the roll. For what values of your parameter does this make sense? Problem 3. The motion of a point P is given parametrically by→ OP = r ( t ) = h 4sin t, 5cos t, 3sin t i ....
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This note was uploaded on 05/14/2010 for the course 18.02A 18.02A taught by Professor Johnbush during the Winter '10 term at MIT.
 Winter '10
 JohnBush

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