A Collection of Problems in Analytical Geometry
Three-Dimensional Analytical Geometry
Published on 6. June 2016
166 pages
978-1-4831-5592-0 (ISBN)
Description
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.
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D.V. Kletenik
Collection of Problems in Analytical Geometry: Three-dimensional Analytical Geometry Pt. 2
Book
12/1966
Pergamon
€1.74
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Content
Author's Preface to the First Russian Edition Author's Preface to the Second Russian EditionPart 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 OrderAppendix: 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 OrderAnswers to Questions and Notes on Solutions
