Chapter 12 Vectors and the Geometry of Space 12-1 & 12-2 Vectors and 3-Dimensional Coordinates 12-3 The Dot Product 12-4 The Cross Product 12-5 Equations of Lines and Planes 12-6 Cylinders and Quadric Surfaces 12-7 Cylindrical and Spherical Coordinates (4th ed.) SDUHSD Abby Brown Calculus III/D SDSU Math 252 www.abbymath.com San Diego, CA The following notes are for the Calculus D (SDSU Math 252) classes I teach at Torrey Pines High School. I wrote and modified these notes over several semesters. The explanations are my own; however, I borrowed several examples and diagrams from the textbooks* my classes used while I taught the course. Over time, I have changed some examples and have forgotten which ones came from which sources. Also, I have chosen to keep the notes in my own handwriting rather than type to maintain their informality and to avoid the tedious task of typing so many formulas, equations, and diagrams. These notes are free for use by my current and former students. If other calculus students and teachers find these notes useful, I would be happy to know that my work was helpful. - Abby Brown * , 6th & 4th editions, James Stewart, ©2007 & 1999 Brooks/Cole Publishing Company, ISBN 0-495-01166-5 & 0-534-36298-2. (Chapter, section, page, and formula numbers refer to the 6th edition of this text.) , 5th edition, Roland E. Larson, Robert P. Hostetler, & Bruce H. Edwards, Calculus: Early Transcendentals *Calculus ©1994 D. C. Heath and Company, ISBN 0-669-35335-3. Name: ___________________________________ www.abbymath.com - Ch. 12 Page 1 of 23
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Chapter 12Vectors and theGeometry of Space
12-1 & 12-2 Vectors and 3-Dimensional Coordinates12-3 The Dot Product12-4 The Cross Product12-5 Equations of Lines and Planes12-6 Cylinders and Quadric Surfaces12-7 Cylindrical and Spherical Coordinates (4th ed.)
SDUHSD
Abby Brown
Calculus III/DSDSU Math 252
www.abbymath.comSan Diego, CA
The following notes are for the Calculus D (SDSU Math 252)classes I teach at Torrey Pines High School. I wrote andmodified these notes over several semesters. Theexplanations are my own; however, I borrowed severalexamples and diagrams from the textbooks* my classes usedwhile I taught the course. Over time, I have changed someexamples and have forgotten which ones came from whichsources. Also, I have chosen to keep the notes in my ownhandwriting rather than type to maintain their informalityand to avoid the tedious task of typing so many formulas,equations, and diagrams. These notes are free for use by mycurrent and former students. If other calculus students andteachers find these notes useful, I would be happy to knowthat my work was helpful. - Abby Brown
* , 6th & 4th editions, James Stewart, ©2007 & 1999Brooks/Cole Publishing Company, ISBN 0-495-01166-5 & 0-534-36298-2.(Chapter, section, page, and formula numbers refer to the 6th edition of this text.)
, 5th edition, Roland E. Larson, Robert P. Hostetler, & Bruce H. Edwards,
Calculus: Early Transcendentals
*Calculus ©1994D. C. Heath and Company, ISBN 0-669-35335-3.
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Note: To find the distance between two parallel planes, choose any point on one of the planes and call that Q. Use Q and the other plane as when finding the distance between a point and a plane.
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