Elementary Vector Geometry

Overview


Dealing primarily with the development of vector algebra as a mathematical tool in geometry, this elementary text features applications to trigonometry, both plane and spherical, and algebra. Appropriate for high school students and college undergraduates, it offers greater insights into theorems by employing vector and analytic proofs, rather than synthetic proofs.
Starting with an overview of elementary operations, the text defines vectors, explores their fundamental ...
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Overview


Dealing primarily with the development of vector algebra as a mathematical tool in geometry, this elementary text features applications to trigonometry, both plane and spherical, and algebra. Appropriate for high school students and college undergraduates, it offers greater insights into theorems by employing vector and analytic proofs, rather than synthetic proofs.
Starting with an overview of elementary operations, the text defines vectors, explores their fundamental properties and linear combinations, and discusses auxiliary point technique and uniqueness of representations. Subsequent chapters examine vectors in coordinate systems, properties and formulas of inner products, and elements of analytic geometry—the straight line, analytic methods of proof, and circles, spheres, and planes. The text concludes with surveys of cross products, plane and spherical trigonometry, and additional geometric concepts, including segments and convexity and linear programming. Exercises appear throughout the book, with solutions at the end.
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Product Details

  • ISBN-13: 9780486466729
  • Publisher: Dover Publications
  • Publication date: 4/4/2008
  • Series: Dover Books on Mathematics Series
  • Pages: 224
  • Sales rank: 1,433,699
  • Product dimensions: 5.38 (w) x 8.50 (h) x 0.42 (d)

Table of Contents


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
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