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TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 251-508 Exam 1 version A, 11 Sep 2008 On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work. Name (print): In all questions, no analytical work — no points. 1. Find an equation of the plane that passes through the line of intersections of planes x + y + z = 1 and 2x − y + z = 3 and passes through the point (1, 1, 2). 2. Which of the following four lines are parallel? Are any of them identical? L1 : L3 : x = 1 − t, y = 2 + t, z = 3 − 2t x−3 =y = 2−z 2 r = h4 + 2t, −2t, 2 + 4ti L4 : r = h1, −1, 3i + th−2, −1, 1i L2 : 3. Find the point of intersection and the angle between the plane x + y + 2z = 6 and the line x = 1 + 2t, y = 2 − t, z = t. α Figure 1: Angle α between a line and a plane 4. Find an equation for the surface consisting of all points that are equidistant from the point (−1, 0, 0) and the plane x = 1. Identify and sketch the surface. 5. (Bonus question +10%) Find the distance from the point (1, 1, 1) to the surface x2 + y 2 + z 2 + 2x − 6z + 9 = 0. Points: /20