chapter 11 vectors and the geometry of space. copyright © houghton mifflin company. all rights...

Chapter 11

Vectors and the Geometry of Space

Copyright © Houghton Mifflin Company. All rights reserved. 11-2

Figure 11.1 and Figure 11.2


Figure 11.4 and Definition of Component Form of a Vector in the Plane


Definitions of Vector Addition and Scalar Multiplication


Figure 11.6


Figure 11.7


Figure 11.8


Theorem 11.1 Properties of Vector Operations


Theorem 11.2 Length of a Scalar Multiple


Theorem 11.3 Unit Vector in the Direction of v


Figure 11.14


Figure 11.15


Figure 11.16


Figure 11.17


Vectors in Space box


Figure 11.19


Figure 11.20


Definition of Parallel Vectors and Figure 11.21


Definition of Dot Product


Theorem 11.4 Properties of the Dot Product


Theorem 11.5 Angle Between Two Vectors and Figure 11.24


Alternative form of dot product and Figure 11.25


Definition of Orthogonal Vectors


Figure 11.26


Definition of Projection and Vector Components and Figure 11.29


Theorem 11.6 Projection Using the Dot Product


Definition of Work and Figure 11.33


Definition of Cross Product of Two Vectors in Space


Theorem 11.7 Algebraic Properties of the Cross Product


Theorem 11.8 Geometric Properties of the Cross Product


Figure 11.36


Theorem 11.9 The Triple Scalar Product


Theorem 11.10 Geometric Property of Triple Scalar Product and Figure 11.41


Figure 11.43


Theorem 11.11 Parametric Equations of a Line in Space


Figure 11.45


Theorem 11.12 Standard Equation of a Plane in Space


Figure 11.47


Figure 11.49


Figure 11.50


Figure 11.51


Theorem 11.13 Distance Between a Point and a Plane and Figure 11.52


Theorem 11.14 Distance Between a Point and a Line in Space and Figure 11.54


Definition of a Cylinder and Figure 11.56


Figure 11.57 and Equations of Cylinders


Quadric Surface


Ellipsoid


Hyperboloid of One Sheet


Hyperboloid of Two Sheets


Elliptic Cone


Elliptic Paraboloid


Hyperbolic Paraboloid


Figure 11.62


Surface of Revolution


The Cylindrical Coordinate System


Figure 11.66


Figure 11.69


Figure 11.70


Figure 11.74


The Spherical Coordinate System


Figure 11.75


Figure 11.76

chapter 11 vectors and the geometry of space. copyright © houghton mifflin company. all rights...

Documents

plane slide

cross product slide

space box slide

geometry of space slide

scalar multiplication

scalar multiple slide

direction of v slide

definition of cross