exam1 - z = 0[6 pts(b Sketch the VVF ¯ r t = 2 t ˆ ı(2-4...

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Math 241 Sections 01** Exam 1 Dr. Justin O. Wyss-Gallifent Directions: Do not simplify unless indicated. No calculators are permitted. Show all work as appro- priate for the methods taught in this course. Partial credit will be given for any work, words or ideas which are relevant to the problem. Please put problem 1 on answer sheet 1 1. Given the following data: P = (1 , 2 , 3) Q = (4 , 10 , 2) ¯ a = 1ˆ ı + 2 ˆ - 2 ˆ k ¯ b = - ı + 2 ˆ + 1 ˆ k (a) Find a vector perpendicular to both -→ PQ and ¯ a . [10 pts] (b) Find the projection of ¯ b onto ¯ a . [5 pts] (c) Find the unit vector in the direction of -→ PQ . [5 pts] Please put problem 2 on answer sheet 2 2. (a) Find the distance between the point (3 , 2 , 1) and the plane 2 x - 3 y + 10 z = 20. Simplify. [12 pts] (b) Find the symmetric equation for the line through the points (2 , - 1 , 4) and (0 , 1 , 4). [8 pts] Please put problem 3 on answer sheet 3 3. (a) Find the point where the line through (0 , 2 , 1) and (3 , 4 , 5) passes through the plane
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Unformatted text preview: z = 0. [6 pts] (b) Sketch the VVF ¯ r ( t ) = 2 t ˆ ı + (2-4 t ) ˆ + t ˆ k for 0 ≤ t ≤ 2. Indicate direction. [6 pts] (c) Give a parametrization of the oriented semi-ellipse shown here. [8 pts] Please put problem 4 on answer sheet 4 4. (a) Assuming a and b are positive constants calculate the curvature of the ellipse [10 pts] ¯ r ( t ) = a cos t ˆ ı + b sin t ˆ at t = π 2 . (b) Calculate the length of the curve ¯ r ( t ) = 2 t ˆ ı + t 2 ˆ + ln t ˆ k for 1 ≤ t ≤ 2. Simplify. [10 pts] Please put problem 5 on answer sheet 5 5. (a) Find the position vector satisfying ¯ a ( t ) = 2ˆ ı + 2 ˆ , ¯ v (0) = 1ˆ ı-2 ˆ and ¯ r (1) = 3ˆ ı + 5 ˆ . [13 pts] (b) Sketch the plane x + 2 y + 3 z = 12. Label the three intercepts with their coordinates. [7 pts] The End...
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This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.

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