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Three-Dimensional Cartesian Coordinate System

Precalculus. Lesson 8.6. Three-Dimensional Cartesian Coordinate System. Quick Review. What you’ll learn about. Three-Dimensional Cartesian Coordinates Distances and Midpoint Formula Equation of a Sphere Planes and Other Surfaces Vectors in Space Lines in Space … and why

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Three-Dimensional Cartesian Coordinate System

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  1. Precalculus Lesson 8.6 Three-Dimensional Cartesian Coordinate System

  2. Quick Review

  3. What you’ll learn about • Three-Dimensional Cartesian Coordinates • Distances and Midpoint Formula • Equation of a Sphere • Planes and Other Surfaces • Vectors in Space • Lines in Space … and why This is the analytic geometry of our physical world.

  4. The Point P(x,y,z) in Cartesian Space

  5. The Coordinate Planes Divide Space into Eight Octants Octant I is the octant in which all three coordinates are positive.

  6. Distance Formula (Cartesian Space)

  7. Midpoint Formula (Cartesian Space)

  8. Example Calculating a Distance and Finding a Midpoint The Distance The Midpoint

  9. Standard Equation of a Sphere

  10. Example Finding the Standard Equation of a Sphere

  11. Equation for a Plane in Cartesian Space

  12. Example Sketching a Plane in Cartesian Space

  13. The Vector v = <v1,v2,v3>

  14. Vector Relationships in Space

  15. Equations for a Line in Space

  16. Example Finding Equations for a Line

  17. Example Finding Equations for a Line

  18. Homework: Text pg695 Exercises # 4-48 (intervals of 4)

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