1697 - Department of Mathematics Math 20300 The City...

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Department of Mathematics The City College of NY Math 20300 Final Exam Spring 2006 No calculators permitted. Answers may be left in terms of radicals, ! , e, etc. and do not need to be simplified unless stated otherwise. Show all work. Part I. Answer all 7 questions. Each is 10 points. 1. Given the points P (1,1,0) , Q (2, " 1,2) , and R ( " 2,2,1) . a) Find the equation of the plane determined by the given points P , Q , R . b) Find the equation of the line, in symmetric form, which is perpendicular to the plane in (a) at the point P . c) Find the area of the triangle PQR . 2. Given that u = f ( x , y , z ) = x 3 y + y 2 e z . a) Evaluate grad u . b) Find the rate of change of u at (1,1,0) in the direction of (3, " 2,6) . c) Find the equation of the tangent plane to the surface x 3 y + y 2 e z = 2 at the point (1,1,0) . 3.
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1697 - Department of Mathematics Math 20300 The City...

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