Chapter Comments

• This chapter introduces 3-space and vectors. While these two topics may seem unrelated at first, it turns out that vector notation allows us to represent and study objects in 3-space more easily than we can without other notations.

• §13.5 will draw on your knowledge of parametric equations to write equations for lines in 3-space. §13.7 will draw on your knowledge of polar coordinates, and your general understanding that some objects are better represented in alternate coordinate systems.

• Keep in mind that as you have studied mathematics through the years you have built up a library of functions and objects with which you are familiar (e.g., you know that y=x² is a parabola with vertex at the origin and opening upward; you know that (x-3)²+(y+1)²=4 is a circle of radius 2 centered at the point (3,-1)). This chapter will introduce you to an analogous set of objects in 3-space (e.g., lines, planes, quadric surfaces). You should spend enough time working with these objects that they become familiar to you in the way that objects in 2-space are.

Chapter Contents

• §13.1 Three-Dimensional Coordinate Systems

• §13.2 Vectors

• §13.3 The Dot Product

• §13.4 The Cross Product

• §13.5 Equations of Lines and Planes

• §13.6 Cylinders and Quadric Surfaces

• §13.7 Cylindrical and Spherical Coordinates

Chapters 13 and 14 Sample Test Items and Sample Solutions

This document is part of the Math 2433: Calculus and Analytic Geometry III course designed for the Independent Study Department in the College of Continuing Education at the University of Oklahoma, Norman.

Go to:

• Calculus III Syllabus

• Table of Contents for Chapter 11: Parametric Equations and Polar Coordinates
• Table of Contents for Chapter 12: Infinite Sequences and Series
• Table of Contents for Chapter 14: Vector Functions