A vector has direction and magnitude both but scalar has only magnitude. Magnitude of a vector a is denoted by | a | or a. It is non-negative scalar.
Equality of Vectors
Two vectors a and b are said to be equal written as a = b, if they have( i) same length( ii) the same or parallel support and( iii) the same sense.
Types of Vectors
( i) Zero or Null Vector A vector whose initial and terminal points are coincident is called zero or null vector. It is denoted by 0.
( ii) Unit Vector A vector whose magnitude is unity is called a unit vector which is denoted by nˆ
( iii) Free Vectors If the initial point of a vector is not specified, then it is said to be a free vector.
( iv) Negative of a Vector A vector having the same magnitude as that of a given vector a and the direction opposite to that of a is called the negative of a and it is denoted by— a.
( v) Like and Unlike Vectors Vectors are said to be like when they have the same direction and unlike when they have opposite direction.
( vi) Collinear or Parallel Vectors Vectors having the same or parallel supports are called collinear vectors.
( vii) Coinitial Vectors Vectors having same initial point are called coinitial vectors.
( viii) Coterminous Vectors Vectors having the same terminal point are called coterminous vectors.
( ix) Localized Vectors A vector which is drawn parallel to a given vector through a specified point in space is called localized vector.