Three-Dimensional Cartesian Coordinate System

1
Chapter 11

• Three-Dimensional Cartesian Coordinate System

2
Quick Review

3
Quick Review Solutions

4
What youll 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.

5
The Point P(x,y,z) in Cartesian Space
6
The Coordinate Planes Divide Space into Eight
Octants
7
Distance Formula (Cartesian Space)

8
Midpoint Formula (Cartesian Space)

9
Example Calculating a Distance and Finding a
Midpoint

10
Example Calculating a Distance and Finding a
Midpoint

11
Standard Equation of a Sphere

12
Drawing Lesson
13
Drawing Lesson (contd)
14
Example Finding the Standard Equation of a Sphere

15
Example Finding the Standard Equation of a Sphere

16
Equation for a Plane in Cartesian Space

17
Warm-up
18
(No Transcript)
19
(No Transcript)
20
Vector Relationships in Space

21
The Vector v ltv1,v2,v3gt
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
Equations for a Line in Space

39
(No Transcript)
40
(No Transcript)
41
Example Finding Equations for a Line

42
Example Finding Equations for a Line

43
Chapter Test

44
Chapter Test