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# OldExam3 - MATH 2008/09B WINTER 2006 AN OLD FINAL EXAM 1....

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MATH 2008/09B WINTER 2006 AN OLD FINAL EXAM 1. (a) If vu and vV are unit vectors, and | vu vV | = 3, Fnd (4 vu vV ) . ( vu + 6 vV ). (b) ±ind the distance from the point P (1 , 1 , 0) to the line passing through the points A (1 , 1 , 1) and B (2 , 0 , 1). 2. (a) Given the lines v r 1 = (1 , 2 , 3) + t (1 , 0 , 5) and v r 2 = (30 , 20 , 10) + t ( c 2 1 , 0 , 3); (i) ±or what value(s) of c are the lines perpendicular? (ii) ±or what value(s) of c are the lines parallel? (b) Let two planes π 1 : x z = 5 and π 2 : x + y 2 z = 11 be given; (i) ±ind the angle between π 1 and π 2 ; (ii) ±ind parametric equations of the line of intersection of π 1 and π 2 . 3. Let the space curve C : r ( t ) = ( t ) v i + (2 t ) v j + ( t 2 ) v k be given and let the point P (1 , 2 , 1) lie on C ; (a) ±ind the unit tangent vector to the curve C at the point P ; (b) ±ind the curvature of C at the point P ; (c) ±ind the radius of the osculating circle at the point P

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## This note was uploaded on 05/26/2010 for the course MATH Math2008 taught by Professor Monadi during the Fall '08 term at Carleton.

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OldExam3 - MATH 2008/09B WINTER 2006 AN OLD FINAL EXAM 1....

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