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TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 251-509 Exam 1 version A, 31 Jan 2008 Name: Points: In all questions, no analytical work — no points. 1. Find the parametric equation of the intersection of two planes: x−y−z = 0 and 2x + y + 2z = 3. /20 2. Find the equation of the plane which contains the points A(1, 1, 0) and B(1, 2, −1) and which does not intersect the line x = 1 + t, y = 2t, z = −1 + t. 3. Sketch the following surfaces and identify them by name (label the axes!): (a) 2x2 + z 2 − y = 1 (b) x2 + 3y 2 = 5 (c) 2x2 + z 2 − y 2 = −1. 4. Calculate the arc length of the curve r(t) = hcos t, sin t, ti from the point (1, 0, 0) to the point of the intersection with the line x = −1, y = −1 + s, z = πs. 5. (Bonus question +10%) Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to yz-plane. Identify the surface.