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Unformatted text preview: ( 15 pts ) (b) An equation for the plane determined by P, Q, and R. ( 15 pts ) (c) The area of the triangle PQR. ( 15 pts ) 4. Show that the two lines intersect. Find the point of intersection and the angle between the lines. ( 15 pts ) L 1 : r (t) = ! 2 + t, 1 + t, 4 + 7t ! L 2 : r (s) = !4 + 5s, 22s, 14s ! 5. Identify and sketch the surfaces given below. ( 15 pts ) (a) y 2 4 = z (b) 2x + 3y + 4z = 12 6. Identify the traces of the given surface in the planes x = k, y = k, and z = k. Then identify the surface and sketch it .( 20 pts ) x 2 4 + z 2 = 9 y 7. The equation z = x 2 + y 2 represents the upper half of a cone which can be written as z ≥ 0, z 2 = x 2 + y 2 . Find the spherical coordinate equation of this cone. ( 15 pts )...
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This note was uploaded on 07/15/2009 for the course MATH 210 taught by Professor Hubscher during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 Hubscher
 Vectors, Dot Product

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