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m203finfall2011 - 1 MATH 203 Final Exam December 2011...

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1 MATH 203 Final Exam, December 2011 Instructions: Complete every question in Part I (Questions 1-7.) Complete three of the five questions in Part II (Questions 8-12). Each question is worth 10 points. No calculators or other electronic devices may be used during the examination. Answers may be left in terms of 7 , sin(3) , π , etc. if needed. Give reasons for all answers. This exam will last 2 hours and 15 minutes. Good luck! 1. (a) Find an equation for the plane through the points A = (0 , 1 , 2), B = (1 , 0 , - 1), and C = (1 , 2 , 3). (b) Find parametric equations for the line through (4 , 1 , 3) and perpendicular to the plane found in (a) above. (c) Let ~v = h 0 , 2 , - 2 i Is the line found in (b) perpendicular to ~v , parallel to ~v or neither of these? 2. At points ( x, y, z ) in a region of space for which x 2 + y 2 1 and z 0, there is an electric charge E ( x, y, z ) = z + z ln( x 2 + y 2 ). (a) Find the rate at which the electric charge is changing at (1 , 0 , 2) in the direction towards the point (4 , 4 , 7).
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