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# Math Math 015

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This 1 page Class Notes was uploaded by Sindhu Furtari on Monday September 19, 2016. The Class Notes belongs to Math 015 at University of Maryland taught by Ben Bezejouh in Fall 2016. Since its upload, it has received 5 views.

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Date Created: 09/19/16

Math 241 Sample Exam 1 A - Time: 50 minutes Name: Write your answer for problem 1 on answer sheet 1. 1. Let u = (1;2;▯1) and v = (0;1;▯2) and A = (1;▯1;2). 1a. (7 pts) Find a vector that is perpendicular to both u and v . Simplify your answer. 1b. (10 pts) Find an equation for the plane perpendicular to u that passes through A. Simplify your answer. 1c. (10 pts) Find the projection of u onto v . Simplify your answer. Write your answer for problem 2 on answer sheet 2. ▯ ▯ 2. The position of a particle is given by r (t) where t > 0. We know that r (1) = (1;▯1;0) and its velocity ▯ 1 p is given by v (tt = (t; ; 2a. (7 pts) Find the acceleration of this particle at time t = 5. ▯ 2b. (10 pts) Find r (t). 2c. (10 pts) Find the length of the path traced out by this particle from t = 1 to t = e. Simplify your answer as much as possible. Write your answer for problem 3 on answer sheet 3. 3. Consider the circle in the plane z = ▯1 centered at (1;1;▯1) whose radius is 1. 3a. (10 pts) Find a parametrization for this circle. p 3 3 3b. (10 pts) Using part (a) ▯nd the unit tangent and unit normal vect2rs o2;▯1). curve at point ( ;1+ Write your answer for problem 4 on answer sheet 4. 4. Consider the lines x + 1 y ▯ 1 ‘1: = = z 2 3 and 8 > x = 2t + 1 < ‘2: y = 3t + 1 > : z = t ▯ 2 4a. (7 pts) Show 1hat 2 and ‘ are parallel. 4b. (10 pts) Find the distance1betw2en ‘ and ‘ . 4c. (10 pts) Find an equation for the plane containing both lines.

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