Important Definitions Related To Vectors

(I) Polar Vectors

Vector which have a starting point or a point of application are called polar vectors.

Example:- Force, Displacement etc

(II) Axial Vectors

Vectors which represent the rotational effect and acts along the axis of rotation are called axial vectors.

Example:- Angular Velocity, Angular Momentum, Torque etc.

(III) Modulus Vectors

The magnitude of a vector is called modulus of that vector.

Example:- For a vector A, It is |A|.

(IV) Unit Vector

A vector having magnitude equal to unity but having a specific direction is called a unit vector.

A unit vector A is written as A^.

A^ = A/|A|

In Cartesian coordinate i^, j^ and k^ are the unit vectors along X,Y and Z Axis respectively.

(V) Null Vector

A vector with magnitude zero and having an arbitrary direction is called null vector.

Example:- The velocity vector of a stationary object.

(VI) Equal Vector

Two vectors are said to be equal if they have equal magnitude and same direction.

(VII) Negative Vector

Two vectors are said to be the negative vectors of each other, if their magnitutes are equal but direction are opposite.

(VIII) Collinear Vectors

Two or more vectors are said to be collinear, when they act along the same lines or parallel lines.

Example:- Tug of war

(IX) Coplanar Vectors

The vectors lying in the same plane are called coplanar vectors.

(X) Co-Initial Vectors

The vectors which have the same initial point are called Co-Initial Vectors.

(XI) Orthogonal Unit Vectors

If two or three unit vectors are perpendicular to each other, they are known as orthogonal unit vectors.

Example:- The unit vectors along X, Y and Z Axis are denoted by i^, j^ and k^. these are orthogonal unit vectors.

(XII) Localised Vectors

Those vectors whose initial point is fixed are known as localised vectors.

Example:- Position vector of a particle, initial point lies at the origin.

(XIII) Non-Localised Vectors

Those vectors whose initial point is not fixed are known as non-localised vectors.

Example:- Velocity vector of a particle moving along a straight line.