1. Vectors and the Geometry of Space
Chapter 11
Vectors and the Geometry of Space

2. Figure 11.1 and Figure 11.2
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3. Figure 11.4 and Definition of Component Form of a Vector in the Plane
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4. Definitions of Vector Addition and Scalar Multiplication
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5. Figure 11.6
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6. Figure 11.7
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7. Figure 11.8
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8. Theorem 11.1 Properties of Vector Operations
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9. Theorem 11.2 Length of a Scalar Multiple
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10. Theorem 11.3 Unit Vector in the Direction of v
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11. Figure 11.14
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12. Figure 11.15
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13. Figure 11.16
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14. Figure 11.17
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15. Vectors in Space box
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16. Figure 11.19
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17. Figure 11.20
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18. Definition of Parallel Vectors and Figure 11.21
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19. Definition of Dot Product
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20. Theorem 11.4 Properties of the Dot Product
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21. Theorem 11.5 Angle Between Two Vectors and Figure 11.24
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22. Alternative form of dot product and Figure 11.25
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23. Definition of Orthogonal Vectors
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24. Figure 11.26
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25. Definition of Projection and Vector Components and Figure 11.29
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26. Theorem 11.6 Projection Using the Dot Product
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27. Definition of Work and Figure 11.33
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28. Definition of Cross Product of Two Vectors in Space
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29. Theorem 11.7 Algebraic Properties of the Cross Product
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30. Theorem 11.8 Geometric Properties of the Cross Product
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31. Figure 11.36
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32. Theorem 11.9 The Triple Scalar Product
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33. Theorem 11.10 Geometric Property of Triple Scalar Product and Figure 11.41
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34. Figure 11.43
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35. Theorem 11.11 Parametric Equations of a Line in Space
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36. Figure 11.45
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37. Theorem 11.12 Standard Equation of a Plane in Space
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38. Figure 11.47
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39. Figure 11.49
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40. Figure 11.50
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41. Figure 11.51
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42. Theorem 11.13 Distance Between a Point and a Plane and Figure 11.52
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43. Theorem 11.14 Distance Between a Point and a Line in Space and Figure 11.54
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44. Definition of a Cylinder and Figure 11.56
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45. Figure 11.57 and Equations of Cylinders
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46. Quadric Surface
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47. Ellipsoid
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48. Hyperboloid of One Sheet
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49. Hyperboloid of Two Sheets
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50. Elliptic Cone
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51. Elliptic Paraboloid
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52. Hyperbolic Paraboloid
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53. Figure 11.62
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54. Surface of Revolution
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55. The Cylindrical Coordinate System
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56. Figure 11.66
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57. Figure 11.69
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58. Figure 11.70
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59. Figure 11.74
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60. The Spherical Coordinate System
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61. Figure 11.75
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62. Figure 11.76
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