Null vector: A vector whose initial and terminal points coincide is called zero vector. Thus the magnitude of zero vector is 0 and has an arbitrary (i.e., no definite) direction. A zero vector (also called a Null vector) is represented by

Proper vector: A non-zero vector is called a proper vector. Thus,

Unit vector: A vector whose magnitude is unity is called a unit vector.

A unit vector in the direction of  (read as cap a).

 

Remark. The unit vector

The unit vectors along x, y, and z directions are represented by respectively.

Co-initial vectors: Two (or more than two) vectors are said to be co-initial vectors if they have the same initial point. Thus  are all co-initial vectors.

Like and unlike vectors: Two (or more than two) vectors are said to be like vectors when they have the same direction irrespective of their magnitudes and vectors having opposite directions are called unlike vectors.

Remark: Like and unlike vectors are also known as co-directional and directional vectors respectively

Equal vectors: Two vectors are said to be equal if they have

(i) The same length

(ii) Same or parallel support, and

(iii) The same sense.

Collinear or Parallel vectors: Two or more vectors are said to be collinear if they have either the same or parallel supports. Thus two or more vectors are collinear if they are parallel to the same line irrespective of their magnitudes.

Co-planar vectors: Two or more vectors are said to be co-planar if either they lie in the same plane or parallel to the same plane.

Free vector: A vector in which the initial point is not specified i.e., there is no restriction to choose its origin is called a free vector.

Axial vector: A vector which gives us sense of rotation e.g., angular velocity

Localized vector: A vector with a fixed initial point is called a localized vector.

Negative of vector: The vector which has the same magnitude as the vector but the direction opposite to that of is called negative vector of .and is written as -.

Thus if represents the vector then will represent the vector -.

Note: It is trivial that

Opposite vectors: The vectors of same magnitude but opposite in direction, are called opposite vectors.

Orthogonal Unit Vectors:  Unit vectors which are in perpendicular direction to each other are known as orthogonal unit vectors. For  example are unit vectors along X,Y and Z axis respectively.

Identical Vectors: Two vectors are said to be identical, if ad only if their magnitudes and directions, both are same.

Polar vectors : These have starting point or point of application . Example displacement and force etc.