THREE DIMENSIONAL GEOMETRY

Plane: Definition, Equation of a plane (Different forms), Angle between two planes, planes through two planes, Distance of a point from a plane, Area of a triangle, Volume of Tetrahedron.

 Straight lines: Introduction, Equations of coordinate axes, Symmetrical form & Non Symmetrical form, Angle between a line and a plane, Perpendicular distance, Intersecting lines, Skew lines, Shortest distance and equation of line of shortest distance, Intersection of three planes.

Sphere: Definition, Equation of a sphere, General equation of a sphere, Centre 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 equation of tangent plane, Angle of intersection of two spheres, Condition of orthogonality of two spheres.

Cone: Cone, Quadratic Cone, Equation of a 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.

Cylinder: Definition, Equation of a cylinder, Enveloping Cylinder, Right Circular Cylinder, Equation of Right Circular Cylinder.

Central Conicoids: Conicoids, Central Conicoid, Standard equation of ellipsoid, hyperboloid of one sheet and hyperboloid of two sheets, Nature and shape of Central conicoids, Tangent line and Tangent planes. Condition of Tangency, Director sphere.

Generating Lines: 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.