SEMSTER-II, PAPER-II
CBCS/ SEMESTER SYSTEM (w.e.f. 2020-21 Admitted Batch)
B.A./B.Sc. MATHEMATICS
THREE DIMENSIONAL ANALYTICAL SOLID GEOMETRY
Syllabus (75 Hours)
Course Outcomes:
After successful completion of this course, the student will be able to; 1.Get the knowledge of planes.
- Basic idea of lines, sphere and
- Understand the properties of planes, lines, spheres and cones. 4.Express the problems geometrically and then to get the
Course Syllabus:
UNIT – I (12 Hours)
The Plane:
Equation of plane in terms of its intercepts on the axis, Equations of the plane through the given points, Length of the perpendicular from a given point to a given plane, System of planes, Bisectors of angles between two planes, Combined equation of two planes.
UNIT – II (12 hrs)
The Line:
Equation of a line; Angle between a line and a plane; The condition that a given line may lie in a given plane; The condition that two given lines are coplanar; Number of arbitrary constants in the equations of straight line; Sets of conditions which determine a line; The shortest distance between two lines; The length and equations of the line of shortest distance between two straight lines.
UNIT – III (12 hrs)
The Sphere-I:
Definition and equation of the sphere; Equation of the sphere through four given points; Plane sections of a sphere; Intersection of two spheres; Equation of a circle; Sphere through a given circle; Intersection of a sphere and a line, Power of a point.
UNIT – IV (12 hrs)
The Sphere-II:
Tangent plane; Plane of contact, Angle of intersection of two spheres; Conditions for two spheres to be orthogonal; Radical plane; Coaxial system of spheres; Simplified from of the equation of two spheres.
UNIT – V (12 hrs)
The Cone:
Definitions of a cone; vertex; guiding curve; generators; Equation of the cone with a given vertex and guiding curve; equations of cones with vertex at origin are homogenous; Condition that the general equation of the second degree should represent a cone, Enveloping cone of a sphere; Vertex of a cone; right circular cone: equation of the right circular cone with a given vertex, axis and semi vertical angle.
Co-Curricular Activities(15 Hours)
Seminar/ Quiz/ Assignments/Three dimensional analytical Solid geometry and its applications/ Problem Solving.
Note: Concentrate Problematic Parts in all above Units
Text Book :
Analytical Solid Geometry by Shanti Narayan and P.K. Mittal, published by S. Chand & Company Ltd. 7th Edition.
Reference Books :
- A text book of Mathematics for BA/B.Sc Vol 1, by V Krishna Murthy & Others, published by
- Chand & Company, New Delhi.
- A text Book of Analytical Geometry of Three Dimensions, by K. Jain and Khaleel Ahmed, published by Wiley Eastern Ltd., 1999.
- Co-ordinate Geometry of two and three dimensions by P. Balasubrahmanyam, K.Y. Subrahmanyam,
G.R. Venkataraman published by Tata-MC Gran-Hill Publishers Company Ltd., New Delhi.
- Solid Geometry by B.Rama Bhupal Reddy, published by Spectrum University
