Calculus & Analytic Geometry (B.A / B.Sc.)
Chapter:07 (Analytic Geometry of Three Dimensions)
In this chapter, we will study the following topics:
- rectangular space coordinates
- right handed system
- left handed system
- xy-plane
- octants
- origin of coordinates
- coordinates of planes
- temperature, energy and mass
- parallelogram law of addition
- directed segment
- position vector
- radius vector of a point p
- the unit vectors i, j, k
- magnitude of a vector, direction cosines
- direction cosines and ratios
- direction components of a line
- free vectors, relation between points
- shifting of origin
- distance between two points
- necessary and sufficient conditions
- the equation of a straight line in vector form
- the equation of a straight line in symmetric form
- the equation of a straight line in parametric form
- reduce to symmetric form
- elimination of the parameter
- distance between the points
- find coordinates of the point dividing internally and externally
- the scalar product or dot product
- physical interpretation of the dot product
- the projection of the segment
- angle between two lines
- vector perpendicular to two given vectors
- the equation of a plane
- the angle between the planes
- distance of a point from a line
- volume of a tetrahedron
- sundry applications
- the area of triangle
- volume of tetrahedron bounded by plane
- the vector product or cross product
- scalar triple product
- vector triple product
- spherical polar coordinates
- cylindrical polar coordinates
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