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# MAT397-2007Fall - MAT 397 Final Exam Nrune ~ S tudent ID I...

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MAT 397 Final Exam December 12 2007 Nrune: ______________________________________________________ ~ ________ ___ Student ID: _____________________ Instructor's Name: Write your answers and show all your work on this test. There are 11 problems on 12 pages (including this cover sheet), for a total of 100 points. To receive full or partial credit, the correct work leading to the correct answer must be written down. Unsupported answers will receive little or no credit. Graphics calculators may be used. Symbolic calculators, such as TI-89 or TI-92, may not be used. i I Problem. Points Score I 1 12 2 8 3 8 I 4 8 5 10 i 6 8 7 8 i 8 8 9 10 10 10 ! 11 10 Total: 100 I

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1. (a) (6 pts) Find the area of the triangle with vertices at the points A(O, 1, -1), B(2, 3,0), and C(3, 3,1). (b) (6 pts) Find an equation of the plane through the points A, B, and C in part (a).
2. (8 pts) Find parametric equations for the line of intersection of the two planes 2x + 5y + z = 4 and x - 3y z 2.

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3. (8 pts) The position of a particle at time t is given by the function r(t) (sin(2t), cos(2t),4t + 1) .
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MAT397-2007Fall - MAT 397 Final Exam Nrune ~ S tudent ID I...

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