IIT (NTSE/Olympiad)  



(a) The physical quantities which have magnitude and direction and which can be added according to the triangle rule, are called vector quantities. Examples : force, linear momentum, electric field, magnetic field etc.
(b) If a physical quantity has magnitude as well as direction but does not add up according to the triangle rule, it will not be called a vector quantity. Example Electric current in a wire has both magnitude and direction but there is no any meaning of triangle rule. Thus, electric current is not a vector quantity.
1.1 Various types of vectors.
(a) Polar Vectors :
Vectors having starting point (as in case of displacement) or point of application (as in case of force) are polar vectors.

(b) Axial vectors
Vectors representing rotational effects and are always along the axis of rotation in accordance with right hand screw rule are axial vectors.
Ex. Angular displacement (θ); Angular velocity (ω) ; Angular acceleration (α) ; Torque (τ) etc.
1.2 Some other types of vectors :
(a) Zero vector :
A vector with zero magnitude is called zero vector.
(b) Proper vector :
A vector with non-zero magnitude is called proper vector.
(c) Like vectors:
Two (or more) vector are called like vectors if their supports are same or parallel and are in the same sense.
(d) Unlike vectors :
Two vectors are called unlike vectors if their supports are same or parallel and are in the opposite sense.
(e) Equal vectors :
Two vectors are called equal (or equivalent) vectors if they have equal magnitude, same or parallel supports and same sense.
(f) Collinear vectors :
Two (or more) vectors are called collinear vectors if they have same or parallel supports.
(g) Coplanar vectors :
Three (or more) vectors are called coplanar vectors if they lie in the same plane or are parallel to the same plane. Two (free) vectors are always coplanar.
(h) Negative vector :
A vector having the same magnitude as that of the given vector but directed in the opposite sense is called the negative of the given vector.
(i) Unit vector :
A vector with magnitude of unity is called unit vector. Unit vector in the direction of a is = a/|a|

IIT (Class X)