`text(1. Zero or null vector:)` A vector whose magnitude is zero is called zero or null vector and it is denoted by `0` or `vec(0)`. The initial and terminal points of the directed line segment representing zero vector are coincident and its direction is arbitrary.

`text(2.Unit vector:)` A vector of unit magnitude is called a unit vector. A unit vector in the direction of `vec(a)` is denoted by `hat(a)` . Thus
`quadquadquadquadquadhat (a) = vec(a) /|vec(a) |`= (Vector `a`)/ (magnitude of `a`)

`text(Note:)`
`(i)` ` |hat (a)| =1`

`(ii)` Unit vectors parallel to `x`- axis, `y`- axis and `z`- axis are denoted by `hat(i) , hat(j)` and `hat(k)` respectively.

`(iii)` Two unit vectors may not be equal unless they have the same direction.

`text(3. Equal Vectors:)` Two vectors `vec(a)` and `vec(b)` are said to be equal , if
`quadquadquadquadquad (a) `` |hat (a)| = |hat (b)|`
`quadquadquadquadquad (b)` they have the same sense of direction

`text(4. Co-initial vectors:)` Vectors having same initial point.

`text(5. Free vectors: )` All such vectors are those which when transformed into space from one point to another point without affecting their magnitude and direction, can be considered as equal. i.e. the physical effects produced by them remains unaltered. e.g. displacement, velocity

`text(6. Localised vectors: )` e.g. force, different physical effect ifline of application is changed.

`text(Note :)` In mathematics we mainly deal with free vectors.