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A Collection of Problems in Analytical Geometry

Three-Dimensional Analytical Geometry

1st Edition - January 1, 1966

Author: D. V. Kletenik

Editors: W. J. Langford, E. A. Maxwell

eBook ISBN:

9 7 8 - 1 - 4 8 3 1 - 5 5 9 2 - 0

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… Read more

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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.

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