# exam1 - APPM 2350 EXAM 1 FALL 2007 INSTRUCTIONS Computers...

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APPM 2350 EXAM 1 FALL 2007 INSTRUCTIONS: Computers, calculators, books, and crib sheets are not permitted. Write your (1) name, (2) instructor’s name, and (3) lecture number (010, 020 or 030) on the front of your bluebook. Work all problems. Start each problem on a new page . Show your work clearly and box your final answer. A correct answer with incorrect or no supporting work may receive no credit, while an incorrect answer with relevant work may receive partial credit. 1. (25 points) Consider the plane P defined by 2 x + 2 y + z = 2 and another plane M that is parallel to P . Let A be a point on the plane M with the coordinates (2 , 2 , 2). (a) Determine the standard equation of plane M . (b) How far is it from plane M to plane P ? (c) Determine the parameterization of a line from point A to the closest point on plane P . (d) Determine the coordinates of the point on plane P closest to point A . 2. (25 points) Consider the movement of a particle traveling on the elliptic path defined by r ( t ) = cos( t ) i + (cos( t ) - 1) j + sin( t ) k for 0 t 2 π .

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• Fall '07
• 10 K, Frenet–Serret formulas

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