A Collection of Problems in Analytical Geometry

A Collection of Problems in Analytical Geometry

Three-Dimensional Analytical Geometry

1st Edition - January 1, 1966

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  • Author: D. V. Kletenik
  • eBook ISBN: 9781483155920

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A Collection of Problems in Analytical Geometry, Part II: Three-Dimensional Analytical Geometry is a collection of problems dealing with analytical geometry in the field of theoretical mechanics. The book discusses rectangular Cartesian coordinates in three-dimensional space and the division of an interval in a given ratio. The sample questions concern problems dealing with isosceles triangles, vertices, and center of gravity of equal masses. The book defines the concept of a vector and then lists problems concerning the triangle law and the scalar product of two vectors. Other problems focus on the equations of a surface and a curve and on questions related to the intersection of three surfaces. The text lists other problems such as the equation of a plane, the direction-vector of a straight line, and miscellaneous problems pertaining to the equations of a plane, of a straight line, and of a sphere in a direction-vector. The selection is useful for professors in analytical geometry and for other courses in physic-mathematics and general engineering.

Table of Contents

  • Author's Preface to the First Russian Edition

    Author's Preface to the Second Russian Edition

    Part II. Three-dimensional Analytical Geometry

    6. Elementary Problems of Three-dimensional Analytical Geometry

    § 27. Rectangular Cartesian Coordinates in Three-Dimensional Space

    § 28. Distance between Two Points. Division of an Interval in a Given Ratio

    7. Vector Algebra

    § 29. The Concept of a Vector. Projection of a Vector

    § 30. Linear Operations on Vectors

    § 31. The Scalar Product of Two Vectors

    § 32. The Vector Product of Two Vectors

    § 33. Scalar Triple Product

    § 34. Vector Triple Product

    8. Equation of a Surface and Equations of Curves

    § 35. Equation of a Surface

    § 36. Equations of a Curve. The Problem of the Intersection of Three Surfaces

    § 37. Equation of a Cylindrical Surface with Generators Parallel to One of the Coordinate Axes

    9. Equation of a Plane. Equations of a Straight Line. Equations of Surfaces of the Second Order

    § 38. The General Equation of a Plane. Equation of a Plane Passing through a Given Point and Having a Given Normal Vector

    § 39. Degenerate Equations of a Plane. Equation of a Plane in Terms of Its Intercepts on the Coordinate Axes

    § 40. The Normal Equation of a Plane. Distance of a Point from a Plane

    § 41. Equations of a Straight Line

    § 42. The Direction-Vector of a Straight Line. The Canonical Equations of a Straight Line. Parametric Equations of a Straight Line

    § 43. Miscellaneous Problems Relating to the Equation of a Plane and the Equations of a Straight Line

    § 44. The Sphere

    § 45. Equations of a Plane, a Straight Line, and a Sphere in Vector Notation

    § 46. Surfaces of the Second Order

    Appendix: Elements of the Theory of Determinants

    § 1. Determinants of the Second Order: Systems of Two Linear Equations in Two Unknowns

    § 2. Homogeneous System of Two First-degree Equations in Three Unknowns

    § 3. Determinants of the Third Order

    § 4. Properties of Determinants

    § 5. Investigation and Solution of a System of Three Linear Equations in Three Unknowns

    § 6. Determinants of the Fourth Order

    Answers to Questions and Notes on Solutions

Product details

  • No. of pages: 166
  • Language: English
  • Copyright: © Pergamon 1966
  • Published: January 1, 1966
  • Imprint: Pergamon
  • eBook ISBN: 9781483155920

About the Author

D. V. Kletenik

About the Editors

W. J. Langford

E. A. Maxwell

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