Elementary Vector Geometry (Dover Books on Mathematics)

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.