Three Dimensional Geometry
This course will enable the students to -
- Demonstrate basic knowledge about three dimensional shapes like sphere, cone , cylinder and central conicoid.
- Understand the concepts & advance topics related to two & three dimensional geometry.
- Study the applications of conics.
- Study the application of sphere, cone and cylinder.
- Study how to trace the curve.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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CMAT 213 |
Three Dimensional Geometry (Theory)
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The students will be able to –
CO24: Construct and differentiate between the three dimensional surfaces like sphere, cone, cylinder and central conicoid. CO25: Determine the equation of a plane section of these surfaces. CO26: Determine the equation of tangent planes and condition of tangency. CO27: Differentiate between the cases of intersection of 3D shapes with line and plane (whether they cut, touch or don't intersect the shape). CO28: Analyze 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
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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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.
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.
Reciprocal cone, Right circular cone, definition and equation of a cylinder, Enveloping cylinder, Right circular cylinder.
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.
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.
- 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.
- 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.
