MATH241 Exam 1 (Wentworth Fall 2008)

# MATH241 Exam 1 (Wentworth Fall 2008) - , 1 , 3) in the...

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MATH 241 – CALCULUS III FIRST MIDTERM EXAM Instructions. Answer each question on a separate answer sheet. Show all your work. Be sure your name, section number, and problem number are on each answer sheet, and that you have copied and signed the honor pledge on the ﬁrst answer sheet. The point value of each problem is indicated. The exam is worth a total of 100 points (each problem is worth 20 points). Be sure to go on to subsequent problems even if there is some part you cannot do. Please leave answers such as 5 2 in terms of radicals and do not convert to decimals. You may not use calculators, notes, or any other form of assistance on this exam. (1) For this problem let u = ˆ i + ˆ j - ˆ k , and v = - ˆ i + 2 ˆ j + 3 ˆ k . (a) Compute u · v . (b) Compute u × v . (c) Find the equation of the line through the point (2
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Unformatted text preview: , 1 , 3) in the direction of v . (d) Find a nonzero vector orthogonal to u and parallel to the plane given by the equation: 2 y + 3 z = x + 1. (2) What is the distance to the origin of the plane containing the points (1 , , 1), (0 , 1 , 1), and (2 , 1 , 0)? (3) Find the position at time t of an object that starts from the point (0 , 1 , 0) at an initial velocity v = 2 ˆ k , and with acceleration vector a =-cos t ˆ i-sin t ˆ j + ˆ k . (4) Compute the length of the curve given by: r ( t ) = cos 3 t ˆ i + sin 3 t ˆ j , 0 ≤ t ≤ 3 π/ 4. (5) Find a parametrization of the portion of the curve given by the equation: x 2 + y 2 + 2 y = 3 and lying between the points ( √ 3 , 0) and (0 , 1). Date : September 29, 2008....
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## This note was uploaded on 11/11/2008 for the course MATH MATH241 taught by Professor Wentworth during the Winter '08 term at Maryland.

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