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