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