Three Dimensional Geometry

Paper Code: 
CMAT212
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 & advance topics related to two & three dimensional geometry.
  3. Study the applications of conics.
  4. Study the application of sphere, cone and cylinder.
  5. Study how to trace the curve. 

Course Outcomes (COs):

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

CMAT 212

Three Dimensional Geometry

(Theory)

 

 

 

 

 

 

The students will be able to –

 

CO26: Construct and differentiate between the three dimensional surfaces like sphere, cone, cylinder and central conicoid.

CO27: Determine the equation of a plane section of these surfaces.

CO28: Determine the equation of tangent planes and condition of tangency.

CO29: Differentiate between the cases of intersection of 3D shapes with line and plane (whether they cut, touch or don't intersect the shape).

CO30: Analyse the concept of ruled and skew surfaces, generating lines on ruled surfaces.

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Field trips

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

 

Unit I: 
I
9.00
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: 
II
9.00
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: 
III
9.00
Reciprocal cone, Right circular cone, Definition and equation of a cylinder, Enveloping cylinder, Right circular cylinder.
 
Unit IV: 
IV
9.00
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: 
V
9.00
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.
 
Academic Year: 
2022-2023
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