Vectors
Day 1: Definitions, Null vector, Unit vector, Like/Unlike vectors, Parallel vectors, Position vector, Collinear vectors, Coplanar vectors, Co-initial vectors, Free vectors, Localised vectors, Equal vectors,Polygon law of addition, Vector Addition, Multiplication Vector, Position Vector of a Point.Day 2: Section Formula, Internal division, External division, Coplanar Vectors, Components of a Vector in Two Dimension, Components of a Vector (AB) ⃗ in terms of Co-ordinates of A and B, Addition, Subtraction Multiplication of a Vector by Equality in Terms, Components of a Vector in Three Dimensions, Co linearity of Vectors, Co linearity of Points, Linearly Dependent and Independent Vectors.
Day 3: Product of Two Vectors, Scalar (or Dot) product of two vectors, Properties of Scalar product, Application of Dot Product on Plane Trigonometry.
Day 4: Vector (or Cross) Product of two Vectors, Properties.
Day 5: Scalar Triple Product, Properties, Vector Triple Product, Tetrahedron, Then the following properties hold.
Day 6: Illustration.
Day 7: Illustration.
Day 8: Illustration.
Three Dimensional Co-ordinate System
Day 1: Three Dimensional Co-ordinate System Position vector of a point on space, G Signs of Co-ordinates of a Point in Various Octants, Distance Formula, Section Formula, Direction Cosines and Direction Ratio’s of a Vector, Co-ordinates of P are (r cos〖α ,r cosβ,r cosγ 〗 ),, Direction Ratios, Directions cosines of parallel vectors, Angle between two vectors in terms of direction cosines and direction ratiosDay 2: Straight Line, Cartesian equation of straight line, Cartesian form, Perpendicular distance of a point from a line (Cartesian form) (Vector form), Reflection or image of a point in a straight line (Cartesian form) (Vector form).
Day 3: Skew Lines.
Day 4: Illustration.
Plane
Day 1: Plane, Equation of a plane passing through a given point, Intercept form of a plane, Vector equation of a plane passing through a given point and normal to a given vector, Cartesian form.Day 2: Equation of plane in normal form vector form, Cartesian form, Angle between the two planes, Angle between a line and a plane, Equation of Plane forming through three given points, Cartesian equivalence, Equation of plane that passes through a point A with position vector a ⃗ and is parallel to given vector (b ) ⃗ and (c ) ⃗, Cartesian form, Equation of any Plane Passing through the Line of Intersection of Plane, +++= and +++=is (+++)+(+++–=), Vector form, Two Sides of a Plane.
Day 3: Distance of a Point from a Plane, Vector form, Cartesian form, Equation of the Planes Bisecting the Angle between two Planes, Vector form, Bisector of the angle between the two planes containing the origin, Bisector of the acute and obtuse angles between two planes, Intersection of a line and a plane, Condition for a line to lie parallel to a plane.
