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Practice Exam #1 for 9/23 Exam

by: Benjamin Mao

Practice Exam #1 for 9/23 Exam MATH241

Marketplace > University of Maryland > MATH241 > Practice Exam 1 for 9 23 Exam
Benjamin Mao
GPA 3.0

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Math exam practice
Calculus III
Study Guide
50 ?




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This 1 page Study Guide was uploaded by Benjamin Mao on Monday September 19, 2016. The Study Guide belongs to MATH241 at University of Maryland taught by Ebrahimian in Fall 2016. Since its upload, it has received 17 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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