Elementary Vector Geometry »

Appropriate for high school and college courses, this elementary text addresses the development of vector algebra as a mathematical tool and features applications to trigonometry and algebra. Exercises, solutions. 1962 edition.

Elementary Operations     1
Introduction
Definition of vector
Fundamental properties
Linear combinations of vectors
Auxiliary point technique
Uniqueness of representations
Vectors in Coordinate Systems     40
Rectangular systems and orientation
Basis vectors and applications
The complex plane
Inner Products     60
Definition
Properties of inner product
Components
Inner product formulas
Work
Analytic Geometry     76
Our point of view
The straight line
Analytic geometry of the line continued
Distance from a point to a line
Analytic method of proof
Circles
Spheres
Planes
Determining a plane by points on it
Distance from a point to a plane
The straight line in three dimensions
Angle between two lines
Intersection of a line with a plane
Angle between a line and a plane
Cross Products     135
Cross products
Triple scalar product
Distance from a point to a plane
Distance between two lines
Triple cross products
Trigonometry     151
Plane trigonometry
Spherical trigonometry
More Geometry     160
Loci defined by inequalities
A few booby traps
Segments and convexity
Linear programming
Theorems arising in more general geometries
Applications of parametric equations to locus problems
Rigid motions
Appendix     204
Answers     206
Index     211