1. Vector : Which physical quantity has magnitude and direction are called vector quantities.
Example : Displacement , Velocity , Acceleration , Force…………………..etc.
2. Characterisation of a Vector :
(i). Length :
(ii). Support :
(iii). Sense :
(iv). Notation of a Vector :
3. Representation of a Vector :
4. Types of Vectors :
(i). Zero Vector or Null Vector :
(ii). Proper Vector :
(iii). Unit Vector :
Note :
(iv). Parallel Vectors :
(v ). Like and Unlike Vectors :
(vi). Collinear Vectors :
(vii). Non – collinear Vectors :
(viii). Co – initial vectors :
(ix). Free Vectors :
(x). Equal Vector : 
(xi). Coplanar Vector :
(xii). Localised Vectors :
(xiii). Reciprocal Vectors :
5. Position Vector of a Point :
6. Addition of two Vectors :
7. Triangle law of addition :
8. Parallelogram law of addition :
9. Addition in component form :
10. Properties of Vector addition : Vector addition has the following properties.
(i). Binary operation :
(ii). Commutativity :
(iii). Associativity :
(iv). Identity :
(v). Additive Inverse :
(vi). Cancellation law :
11. Subtraction of Vectors :
Example :
Note :
12. Vectors in terms of position vectors of end points :
13. Multiplication of a vector by a scalar :
Example :
Note :
Properties Multiplication of a vector by a scalar :
14. Modulus of a Vector :
15. Collinearity of three Points :
16. Relation between two parallel and perpendicular vectors :
17. Direction Cosines of a vector :
18. Co-planar and non – co-planar vectors : Vectors are said to be co-planar if they lie in the same plane or they are parallel to the same plane otherwise they are said to be non – co-planar.
19. Components of a vector in two Dimensions :
20. Components of a vector in three Dimensions :
21. The equation of a straight line :
22. Disector of the angle between two straight lines.
23. Equation of a plane :
Note :
24. Ceva’s Theorem :
25. Menelau’s Theorem :
26. Centroid :
27. Section Formula :
(i). Internal Division :
(ii). External Division :
(iii). Centroid of Triangle :
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