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408DS09assign7 - 4-3 = z-5 Determine whether the lines are...

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M408D Spring 2009 Assignment 7 Due Thursday, April 2 Be sure that you have read and understood sections 13.5, 13.6, 14.1, and 14.2 and worked the assigned text exercises before you complete this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Homework is to be turned in at the beginning of the discussion section. 1. Let L 1 be the line given by symmetric equations x - 1 4 = y - 5 - 4 = z + 1 5 and let L 2 be the line given by symmetric equations x -
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Unformatted text preview: 4-3 = z-5. Determine whether the lines are parallel, intersecting, or skew. 2. Find the equation of the plane through the point (-1 , 4 , 2) and containing the line of intersection of the planes 4 x-y + z = 2 and 2 x + y-2 z = 3. 3. Describe the traces of the surface x 2 + 4 y 2-16 z 2 = 1 in the coordinate planes and sketch the surface. 4. Find a vector function representing the curve of intersection of the paraboloid z = 4 x 2 + y 2 and the parabolic cylinder y = x 2 . 5. Find parametric equations for the tangent line to the curve ~ r ( t ) = (ln t ) ~ i + (2 t ) ~ j + t 2 ~ k at the point corresponding to t = 1. 1...
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