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x y z 4x 4z 0 x 4x 4 y z 4z 4 4 4# b b b c b b b b c b ba b a b x 2 y 0 z 2 8 the center is at 2 0 2 and the radius is 8 b b c b c c a b a b a b a b # 56. x y 7 z 49a b a b b b c b b b b b #1 2 16 2 3 81 55. x y 1 z 5 4a b a b a b a b a bc b c b c b b b c # 53. P P 0 5 0 3 0 2 38k k a b a b a b " # c b c b b 47. P P 2 0 2 0 2 0 3 4 2 3k k a b a b a b " # c b c c b c c 46. P P 2 3 3 4 4 5 3k k a b a b a b " # c b c b c 45. P P 4 1 2 4 7 5 49 7k k a b a b a b " # c b c c b c 44. Section 12.1 Three-Dimensional Coordinate Systems 717 43. P P 2 1 5 1 0 5 50 5 2k k a b a b a b " # b b c b c Copyright 2010 Pearson Education Inc. P P 3 1 3 1 0 1 9 3k k a b a b a b " # c b c b c 42. (a) x 1 y 1 z 1 1 (b) x 1 y 1 z 1 1a b a b a b a b a b a bc b c b c c b c b c # 40. x y z 1 4 and x y z 1 4 x y z 1 x y z 1 z 0, x y 3# b b c b b b b b c b b b b a b a b a b a b 35. x y z 25, z 3 x y 16 in the plane z 3# b b b 34. x y z x y 2 z x y z x y 2 z y y 4y 4 y 1 a b a b# b b b c b b b b c b c b 33. (a) x 3 y 4 1, z 1 (b) y 4 z 1 1, x 3a b a b a b a bb b c c b c c# (c) x 3 z 1 1, y 4a b a bb b c # 31. (a) x y 2 4, z 0 (b) y 2 z 4, x 0 (c) x z 4, y 2# b c c b b a b a b 30.

c (b) All points that lie on the curve z y in the plane x 2. (a) All the points the lie on the plane z 1 y. # (b) The region on or to the left of the parabola x y in the xy-plane and all points above it that are 2 units or less away # from the xy-plane. (a) The region on or inside the parabola y x in the xy-plane and all points above this region. (a) The line y x in the xy-plane (b) The plane y x consisting of all points of the form (x x z) 23. (a) The solid enclosed between the sphere of radius 1 and radius 2 centered at the origin (b) The solid upper hemisphere of radius 1 centered at the origin 22. 716 Chapter 12 Vectors and the Geometry of Space (c) A solid cylindrical column of radius 1 whose axis is the z-axis 21. (a) The circumference and interior of the circle x y 1 in the xy-plane# b (b) The circumference and interior of the circle x y 1 in the plane z 3# b Copyright 2010 Pearson Education Inc.

(a) The solid ball of radius 1 centered at the origin (b) The exterior of the sphere of radius 1 centered at the origin 20. (a) The slab bounded by the planes x 0 and x 1 (b) The square column bounded by the planes x 0, x 1, y 0, y 1 (c) The unit cube in the first octant having one vertex at the origin 19. (a) The first quadrant of the xy-plane (b) The fourth quadrant of the xy-plane 18. The circle formed by the intersection of the sphere x y z 4 and the plane y x.# b b 15. The ellipse formed by the intersection of the cylinder x y 4 and the plane z y.# b 14. The circle x z 9 in the plane y 4# b c 11. The circle x y 4 in the plane z = 2# b c 7. The line through the point 1 0 0 parallel to the z-axisa b 5. The line through the point 1 0 0 parallel to the y-axisa bc 3. The line through the point 2 3 0 parallel to the z-axisa b 2. CHAPTER 12 VECTORS AND THE GEOMETRY OF SPACE 12.1 THREE-DIMENSIONAL COORDINATE SYSTEMS 1. Thomas Calculus Early Transcendentals 14th Edition Isbn 439020 Ebookschoice Calculus Math Methods Online Math Courses FULL-COLOR illustrations make the text even more visually appealing and user-friendly.
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