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OldExam1 - MATH 2008/09B WINTER 2005 AN OLD FINAL EXAM 1....

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MATH 2008/09B WINTER 2005 AN OLD FINAL EXAM 1. Determine whether the lines: v r 1 = (2 , 1 , 0) + t (1 , 2 , 3) and v r 2 = ( 1 , 1 , 2) + s ( 2 , 1 , 1) are parallel, intersecting, or skew. If they intersect, Fnd the point of intersection. 2. (a) ±ind a vector equation of the line of intersection of the planes 2 x y + z = 3 and 3 x + 2 y + z = 4. (b) ±ind the scalar(cartesian) equation of the plane that is perpendicular to the line obtained in (a) and contains the point (1 , 1 , 1). 3. The position vector of an object is given by r ( t ) = ( t ) v i + p 1 2 t 2 P v j + p 1 3 t 3 P v k ; (a) ±ind the unit tangent vector at the point p 1 , 1 2 , 1 3 P ; (b) ±ind the tangential and normal components of the acceleration vector at the point p 1 , 1 2 , 1 3 P ; (c) Use (a) and (b) to Fnd the unit normal vector at the point p 1 , 1 2 , 1 3 P . 4. Given the function f ( x, y ) = sin( x 2 + y 2 ) x 2 + y 2 if ( x, y ) n = (0 , 0) and f (0 , 0) = 7; (a) Determine if

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This note was uploaded on 05/26/2010 for the course MATH Math2107 taught by Professor Lanihaque during the Fall '10 term at Carleton.

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OldExam1 - MATH 2008/09B WINTER 2005 AN OLD FINAL EXAM 1....

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