Three Dimensional Geometry

Paper Code: 
25CMAT213
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to -
 
  1. Demonstrate basic knowledge about three dimensional shapes like sphere, cone, cylinder and central conicoid.
  2. Understand the concepts & advanced topics related to two & three dimensional geometry.
  3. Study the applications of conics.
  4. Study the application of the sphere, coneand cylinder.
  5. Study how to trace the curve. 

 

Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

 

25CMAT

213

 

 

Three Dimensional Geometry

(Theory)

 

 

 

 

CO34: Determine the equation of a sphere under various conditions and check for the orthogonality of spheres.

CO35: Identify as well as construct the equation of cone under given conditions and analyze the properties of the origin vertexed cone and enveloping cones.

CO36: Determine the equation of a right circular cone, reciprocal cone, enveloping cylinder and right circular cylinder under given conditions.

CO37: Differentiate between the central conicoid shapes like ellipsoid and hyperboloid. Their intersection with a line and a plane.

CO38: Analyze the concept of ruled and skew surfaces, generating lines on ruled surfaces.

CO39: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions

 

 

 

Quiz, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
Sphere
12.00
Definition, General equation of a sphere, Center and radius of a sphere, Great circle, Equation of circle, Diameter form of the equation of a sphere, Tangent line and tangent plane of a sphere, Condition of tangency for a line and tangent plane, Angle of intersection of two spheres, Condition of orthogonality of two spheres.
 
Unit II: 
Cone
12.00
Condition for general equation of second degree to represent various form of surfaces, Cone, Quadratic cone, Enveloping cone, Condition for general equation of second degree to represent a cone, Intersection with a line and a plane, Angle between the intersecting lines of cone, Tangent plane.
 
Unit III: 
Special Cone and Cylinder
12.00

Reciprocal cone, Right circular cone, definition and equation of a cylinder, Enveloping cylinder, Right circular cylinder.

Unit IV: 
Central Conicoid
12.00
Conicoid, Central conicoid, Standard equation of ellipsoid, hyperboloid of one sheet and hyperboloid of two sheets, Nature and shape of central conicoid, Intersection of a line and a central conicoid, Tangent line and tangent plane, Condition of tangency, Director sphere.
 

 

Unit V: 
Generating Lines
12.00
Developable surface, Skew surface, Generating lines of central conicoid, System of generating lines, Equation of generator through one point and two points on the principle elliptic section of a hyperboloid of one sheet.
 

 

Essential Readings: 
  • N. Saran and R.S. Gupta, Analytical Geometry of Three Dimensions, Pothisala Pvt. Ltd, Allahabad, 1992.
  • G.C.Sharma and Madhu Jain, Co-ordinate Geometry (2-D&3-D), Galgotia Publication, Dariyaganj, New Delhi, 1996.
  • Shanti Narayan and P.K. Mittal, Analytical Solid Geometry, S. Chand & Co. Pvt. Ltd. New Delhi, 2007.
  • Brahma Nand, B.S. Tyagi and Bhudev Sharma, Coordinate Solid Geometry, Kedar Nath Ram Nath, Meerut, 2020.
 
References: 
  • T. A. Chishti and S. Pirzada, Analytical Solid Geometry, Orient Black Swan India, 2007.
  • S.L. Loney, The Elements of Coordinate Geometry, Macmillan and Co., London, 2016.
  • R.J.T. Bell, Elementary Treatise on Coordinate Geometry of Three Dimensions, Macmillan India Ltd, 2018.
  • P. R. Vittal, Analytical Geometry: 2D and 3D, Pearson Education India, 2013.

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Academic Year: 
2025-2026
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