Geometry & Vector Analysis PDF
331 Pages·2021·3.6183 MB·other
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SYLLABUS- GEOMETRY & VECTOR ANALYSIS,
PAPER III: GEOMETRY AND VECTOR ANALYSIS
Polar Equation of conics: Polar coordinate system, Distance between two points, Polar equation of a Straight line, Polar equation of a circle, Polar equation of a conic, Chords, Tangent and Normal to a conic, Chord of contact, Polar of a point.
Vector Algebra and its Applications to geometry (Plane and Straight Line):
Triple product, Reciprocal vectors, Product of four vectors. General equation of a Plane, Normal and Intercept forms, Two sides of a plane, Length of perpendicular from a point to a plane, Angle between two planes, System of planes.
Direction Cosines and Direction ratios of a line, Projection on a straight line, Equation of a line, Symmetrical and unsymmetrical forms, Angle between a line and a plane, Coplanar lines, Lines of shortest distance, Length of perpendicular from a point to a line, Intersection of three planes, Transformation of coordinates.
Vector Differentiation: Ordinary differentiation of vectors, Applications to mechanics, Velocity and Acceleration, Differential operator-Del, Gradient, Divergence and Curl,
Vector Integration: Line, Surface and volume integrals, Simple applications of Gauss divergence theorem,Green’s theorem and Stokes theorem (without proof).
PAPER III: GEOMETRY AND VECTOR ANALYSIS
Polar Equation of conics: Polar coordinate system, Distance between two points, Polar equation of a Straight line, Polar equation of a circle, Polar equation of a conic, Chords, Tangent and Normal to a conic, Chord of contact, Polar of a point.
Vector Algebra and its Applications to geometry (Plane and Straight Line):
Triple product, Reciprocal vectors, Product of four vectors. General equation of a Plane, Normal and Intercept forms, Two sides of a plane, Length of perpendicular from a point to a plane, Angle between two planes, System of planes.
Direction Cosines and Direction ratios of a line, Projection on a straight line, Equation of a line, Symmetrical and unsymmetrical forms, Angle between a line and a plane, Coplanar lines, Lines of shortest distance, Length of perpendicular from a point to a line, Intersection of three planes, Transformation of coordinates.
Vector Differentiation: Ordinary differentiation of vectors, Applications to mechanics, Velocity and Acceleration, Differential operator-Del, Gradient, Divergence and Curl,
Vector Integration: Line, Surface and volume integrals, Simple applications of Gauss divergence theorem,Green’s theorem and Stokes theorem (without proof).
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