23UMATC23 Analytical Geometry of Three Dimension Syllabus:

23UMATC23 Analytical Geometry of Three Dimension Syllabus – Annamalai University UG Syllabus Regulation 2023-24

Objectives of the Course

Necessary skills to analyze characteristics and properties of two- and three-dimensional geometric shapes.

  • To present mathematical arguments about geometric relationships.
  • To solve real world problems on geometry and its applications.

UNIT-I: 

Rectangular cartesian co-ordinates: direction cosines of a line- Angle between two lines-Projections-Direction cosines-Direction ratios- Conditions for perpendicularity and parallelism

UNIT-II:

System of Planes-Length of the perpendicular–Orthogonal projection.

UNIT-III: 

Representation of line–angle between a line and a plane – co – planar lines–shortest distance between two skew lines –length of the perpendicular–intersection of three planes.

UNIT-IV:

Equation of a sphere-general equation-section of a sphere by a plane-equation of the circle- tangent plane- angle of intersection of two spheres- condition for the orthogonality- radical plane.

UNIT-V:

The Central Quadrics and Cone- The equation of a surface. Cone. Right circular cone. Intersection of a straight line and a quadric cone. Tangent plane and normal. Condition that the cone has three mutually perpendicular generators. Cylinder Enveloping Cylinder.

Recommended Text

K. Manickavachagom Pillai and T. Natarajan. A Text Book Of Analytical Geometry (Part II-Three Dimensions)Viswanathan (Printers & Publishers) Pvt. Ltd.

Unit I Chapter 1 :  Sec (1-12)

Unit II Chapter 2: Sec (13-23)

Unit III Chapter 3: Sec (24-30,33)

Unit IV Chapter 4: Sec (35-42)

Unit V Chapter 5: Sec (43-49)

Reference Books

  • S. L. Loney, Co-ordinate Geometry.
  • Robert J. T. Bell, Co-ordinate Geometry of Three Dimensions.
  • William F. Osgood and William C. Graustein, Plane and Solid Analytic Geometry, Macmillan Company, New York, 2016.Calculus and Analytical Geometry, G.B. Thomas and L. Finny, Pearson Publication, 9th Edition, 2010.
  • Robert C. Yates, Analytic Geometry with Calculus, Prentice Hall, Inc., New York, 1961.
  • Earl W. Swokowski and Jeffery A. Cole, Algebra and Trigonometry with Analytic Geometry, Twelfth Edition, Brooks/Cole, Cengage Learning, CA, USA, 2010.
  • William H. McCrea, Analytical Geometry of Three Dimensions, Dover Publications, Inc, New York, 2006.