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192prelim1

# 192prelim1 - Mathematics 192 Fall 2004 Preliminary...

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Mathematics 192 Fall 2004 Preliminary Examination I Thursday, September 30, 2004 7:30-9:00 PM No calculators. An 8.5 × 11 in. sheet of paper, with information on both sides, is allowed. Please make sure to give adequate reasons for all your answers. 1. (a) (6 points) Find the coordinates of the point of intersection of the two lines: L 1 : x = 1 y = 0 z = 8 t + 7 L 2 : x = s + 2 y = 3 s + 3 z = 2 s + 1 (b) (6 points) Find an equation of the plane that contains the two lines L 1 and L 2 . . (c) (5 points) Find the cosine of the angle between the lines L 1 and L 2 . 2. (a) (5 points) Find an equation of the plane that is orthogonal (perpendicular) to the line L : L : x = t y = t + 3 z = t and passes through the point P (2,0,2). (b) (7 points) Find an equation for each plane that is orthogonal to L and is at a distance 3 from the point P (2,0,2). (c) (5 points) Find parametric equations of the line that passes through the points Q (0,3,0) and R (1,4,-1). 3. A point P is moving on a curve: x = t cos t, y = t sin t, z = t

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