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Table of Contents
Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Chapter 1: Plane
1.1: Definition
1.2: General Equation of the First Degree in x, y, z Represents a Plane
1.3: Transformation of General form to Normal Form
1.4: Direction Cosines of the Normal to a Plane
1.5: Equation of a Plane Passing through a Given Point
1.6: Equation of the Plane in Intercept Form
1.7: Reduction of the General Equation of the Plane to the Intercept Form
1.8: Equation of a Plane Passing through three Points
1.9: Equation of any Plane Parallel to a Given Plane
1.10: Equation of Plane Passing through the Intersection of Two Given Planes
1.11: Equation of the Plane Passing through the Intersection
1.12: Angle between Two Planes
1.13: Position of the Origin w.r.t. the Angle between Two Planes
1.14: Two Sides of a Plane
1.15: Length of the Perpendicular from a Point to a Plane
1.16: Bisectors of Angles between Two Planes
1.17: Pair of Planes
1.18: Orthogonal Projection on a Plane
1.19: Volume of a Tetrahedron
Exercise
Chapter 2: Straight Line
2.1: Representation of Line (Introduction)
2.2: Equation of a Straight Line in the Symmetrical Form
2.3: Equation of a Straight Line Passing through Two Points
2.4: Transformation from the Unsymmetrical to the Symmetrical Form
2.5: Angle between a Line and a Plane
2.6: Point of Intersection of a Line and a Plane
2.7: Conditions for a Line to Lie in a Plane
2.8: Condition of Coplanarity of Two Straight Lines
2.9: Skew Lines and the Shortest Distance between Two Lines
2.10: Equation of Two Skew Lines in Symmetric Form
2.11: Intersection of Three Planes
Exercise
Chapter 3: Sphere
3.1: Definition
3.2: Equation of Sphere in Vector Form
3.3: General Equation of the Sphere.
3.4: Equation of Sphere Whose End-Points of a Diameter are Given
3.5: Equation of a Sphere Passing through the Four Points
3.6: Section of the Sphere by a Plane
3.7: Intersection of Two Spheres
3.8: Intersection of Sphere S and Line L
3.9: Tangent Plane
3.10: Equation of the Normal to the Sphere
3.11: Orthogonal Sphere
Exercise
Chapter 4: Cone
4.1: Definition
4.2: Equation of a Cone with a Conic as Guiding Curve
4.3: Enveloping Cone to a Surface
4.4: Equation of the Cone whose Vertex is the Origin is Homogeneous
4.5: Intersection of a Line with a Cone
4.6: Equation of a Tangent Plane at (α, β, γ) to the Cone with Vertex Origin
4.7: Conditions for Tangency
4.8: Right Circular Cone
Exercise
Chapter 5: Cylinder
5.1: Definition
5.2: Equation of the Cylinder whose Generators Intersec tthe Given Conic
5.3: Enveloping Cylinder
5.4: Right Circular Cylinder
Exercise
Chapter 6: Central Conicoid
6.1: Definition
6.2: Intersection of a Line with the Central Conicoid
6.3: Tangent Lines and Tangent Plane at a Point
6.4: Condition of Tangency
6.5: Normal to Central Conicoid
6.6: Plane of Contact
6.7: Polar Plane of a Point
Exercise
Chapter 7: Miscellaneous Examples using MATLAB
Index
About the Authors.
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Chapter 1: Plane
1.1: Definition
1.2: General Equation of the First Degree in x, y, z Represents a Plane
1.3: Transformation of General form to Normal Form
1.4: Direction Cosines of the Normal to a Plane
1.5: Equation of a Plane Passing through a Given Point
1.6: Equation of the Plane in Intercept Form
1.7: Reduction of the General Equation of the Plane to the Intercept Form
1.8: Equation of a Plane Passing through three Points
1.9: Equation of any Plane Parallel to a Given Plane
1.10: Equation of Plane Passing through the Intersection of Two Given Planes
1.11: Equation of the Plane Passing through the Intersection
1.12: Angle between Two Planes
1.13: Position of the Origin w.r.t. the Angle between Two Planes
1.14: Two Sides of a Plane
1.15: Length of the Perpendicular from a Point to a Plane
1.16: Bisectors of Angles between Two Planes
1.17: Pair of Planes
1.18: Orthogonal Projection on a Plane
1.19: Volume of a Tetrahedron
Exercise
Chapter 2: Straight Line
2.1: Representation of Line (Introduction)
2.2: Equation of a Straight Line in the Symmetrical Form
2.3: Equation of a Straight Line Passing through Two Points
2.4: Transformation from the Unsymmetrical to the Symmetrical Form
2.5: Angle between a Line and a Plane
2.6: Point of Intersection of a Line and a Plane
2.7: Conditions for a Line to Lie in a Plane
2.8: Condition of Coplanarity of Two Straight Lines
2.9: Skew Lines and the Shortest Distance between Two Lines
2.10: Equation of Two Skew Lines in Symmetric Form
2.11: Intersection of Three Planes
Exercise
Chapter 3: Sphere
3.1: Definition
3.2: Equation of Sphere in Vector Form
3.3: General Equation of the Sphere.
3.4: Equation of Sphere Whose End-Points of a Diameter are Given
3.5: Equation of a Sphere Passing through the Four Points
3.6: Section of the Sphere by a Plane
3.7: Intersection of Two Spheres
3.8: Intersection of Sphere S and Line L
3.9: Tangent Plane
3.10: Equation of the Normal to the Sphere
3.11: Orthogonal Sphere
Exercise
Chapter 4: Cone
4.1: Definition
4.2: Equation of a Cone with a Conic as Guiding Curve
4.3: Enveloping Cone to a Surface
4.4: Equation of the Cone whose Vertex is the Origin is Homogeneous
4.5: Intersection of a Line with a Cone
4.6: Equation of a Tangent Plane at (α, β, γ) to the Cone with Vertex Origin
4.7: Conditions for Tangency
4.8: Right Circular Cone
Exercise
Chapter 5: Cylinder
5.1: Definition
5.2: Equation of the Cylinder whose Generators Intersec tthe Given Conic
5.3: Enveloping Cylinder
5.4: Right Circular Cylinder
Exercise
Chapter 6: Central Conicoid
6.1: Definition
6.2: Intersection of a Line with the Central Conicoid
6.3: Tangent Lines and Tangent Plane at a Point
6.4: Condition of Tangency
6.5: Normal to Central Conicoid
6.6: Plane of Contact
6.7: Polar Plane of a Point
Exercise
Chapter 7: Miscellaneous Examples using MATLAB
Index
About the Authors.