ISM_T11_C12_A - CHAPTER 12 VECTORS AND THE GEOMETRY OF...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
CHAPTER 12 VECTORS AND THE GEOMETRY OF SPACE 12.1 THREE-DIMENSIONAL COORDINATE SYSTEMS 1. The line through the point ( ) parallel to the z-axis #ß $ß ! 2. The line through the point ( 1 0 ) parallel to the y-axis ß ß ! 3. The x-axis 4. The line through the point (1 ) parallel to the z-axis ß !ß ! 5. The circle x y 4 in the xy-plane # # œ 6. The circle x y 4 in the plane z = 2 # # œ 7. The circle x z 4 in the xz-plane # # œ 8. The circle y z 1 in the yz-plane # # œ 9. The circle y z 1 in the yz-plane # # œ 10. The circle x z 9 in the plane y 4 # # œ œ 11. The circle x y 16 in the xy-plane # # œ 12. The circle x z 3 in the xz-plane # # œ 13. (a) The first quadrant of the xy-plane (b) The fourth quadrant of the xy-plane 14. (a) The slab bounded by the planes x 0 and x 1 œ œ (b) The square column bounded by the planes x 0, x 1, y 0, y 1 œ œ œ œ (c) The unit cube in the first octant having one vertex at the origin 15. (a) The solid ball of radius 1 centered at the origin (b) The exterior of the sphere of radius 1 centered at the origin 16. (a) The circumference and interior of the circle x y 1 in the xy-plane # # œ (b) The circumference and interior of the circle x y 1 in the plane z 3 # # œ œ (c) A solid cylindrical column of radius 1 whose axis is the z-axis 17. (a) The closed upper hemisphere of radius 1 centered at the origin (b) The solid upper hemisphere of radius 1 centered at the origin 18. (a) The line y x in the xy-plane œ (b) The plane y x consisting of all points of the form (x x z) œ ß ß
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
780 Chapter 12 Vectors and the Geometry of Space 19. (a) x 3 (b) y 1 (c) z 2 œ œ œ 20. (a) x 3 (b) y 1 (c) z 2 œ œ œ 21. (a) z 1 (b) x 3 (c) y 1 œ œ œ 22. (a) x y 4, z 0 (b) y z 4, x 0 (c) x z 4, y 0 # # # # # # œ œ œ œ œ œ 23. (a) x (y 2) 4, z 0 (b) (y 2) z 4, x 0 (c) x z 4, y 2 # # # # # # œ œ œ œ œ œ 24. (a) (x 3) (y 4) 1, z 1 (b) (y 4) (z 1) 1, x 3 œ œ œ œ # # # # (c) (x 3) (z 1) 1, y 4 œ œ # # 25. (a) y 3, z 1 (b) x 1, z 1 (c) x 1, y 3 œ œ œ œ œ œ 26. x y z x (y 2) z x y z x (y 2) z y y 4y 4 y 1 È È # # # # # # # # # # # # # # œ Ê œ Ê œ Ê œ 27. x y z 25, z 3 x y 16 in the plane z 3 # # # # # œ œ Ê œ œ 28. x y (z 1) 4 and x y (z 1) 4 x y (z 1) x y (z 1) z 0, x y 3 # # # # # # # # # # # # # # œ œ Ê œ Ê œ œ 29. 0 z 1 30. 0 x 2, 0 y 2, 0 z 2 Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ 31. z 0 32. z 1 x y Ÿ œ È # # 33. (a) (x 1) (y 1) (z 1) 1 (b) (x 1) (y 1) (z 1) 1 # # # # # # 34. 1 x y z 4 Ÿ Ÿ # # # 35. P P 3 1 3 1 0 1 9 3 k k a b a b a b É È " # # # # œ œ œ 36. P P 2 1 5 1 0 5 50 5 2 k k a b a b a b É È È " # # # # œ œ œ 37. P P 4 1 2 4 7 5 49 7 k k a b a b a b É È " # # # # œ œ œ 38. P P 2 3 3 4 4 5 3 k k a b a b a b É È " # # # # œ œ 39. P P 2 0 2 0 2 0 3 4 2 3 k k a b a b a b É È È " # # # # œ œ œ 40. P P 0 5 0 3 0 2 38 k k a b a b a b É È " # # # # œ œ 41. center ( 2 0 2), radius 2 2 42. center , radius ß ß ß ß È ˆ " " " # # # # È 21 43. center 2 2 2 , radius 2 44. center , radius Š È È È È ˆ ß ß ß " " 3 3 3 29 È
Image of page 2
Section 12.2 Vectors 781 45. (x 1) (y 2) ( 3) 14 46. x (y 1) (z 5) 4 D œ œ # # # # # # 47. (x 2) y z 3 48. x (y 7) z 49 œ œ # # # # # # 49. x y z 4x 4z 0 x 4x 4 y z 4z 4 4 4 # # # # # # œ Ê œ a b a b (x 2) (y 0) (z 2) 8 the center is at ( 2 0 2) and the radius is 8 Ê œ Ê ß ß # # # # Š È È 50. x y z 6y 8z 0 x y 6y 9 z 8z 16 9 16 (x 0) (y 3) (z 4) 5 # # # # # # # # # # œ Ê œ Ê œ a b a b the center is at (0 3 4) and the radius is 5 Ê ß ß 51. 2x 2y 2z x y z 9 x x y y z z # # # # # # " " " # # # # œ Ê œ 9 x x y y z z x y z Ê œ Ê œ ˆ ˆ
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern