Calculus D Notes

Name: ___________________________________
www.abbymath.com - Ch. 12
Page 1 of 23
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.)
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
SDUHSD Calculus III/D
SDSU Math 252
Abby Brown
www.abbymath.com
San Diego, CA
*Calculus: Early Transcendentals, 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.)
*Calculus, 5th edition, Roland E. Larson, Robert P. Hostetler, & Bruce H. Edwards, ©1994
D. C. Heath and Company, ISBN 0-669-35335-3.
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 2 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 3 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 4 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 5 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 6 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 7 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 8 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 9 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 10 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 11 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 12 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 13 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 14 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 15 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 16 of 23
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.
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 17 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 18 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 19 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 20 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 21 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 22 of 23
Name: ___________________________________
www.abbymath.com - Ch. 12
Page 23 of 23