A vector which gives position of an object with reference to the origin of a coordinate system is called position vector.
It is represented by a symbol r.
Let the motion of an object in x-y plane with origin at O. Let an object is at point A at any instant t, then OA is the position vector of the object at point A, OA = r.
The position vector provide two information.
(I) It tells us about the minimum distance of an object from the origin O.
(II) It tells about the direction of the object with respect to origin O.
The vector which tells how much and in which direction and object has changed its position in a given interval of time is called displacement vector.
Displacement vector is a straight line joining the initial and final positions and does not depends on the actual path undertaken by the object between the two positions.
Let an object is moving in x-y plane. Let it is at point A at any stand t and at any point B at any letter time t’. Then vector AB is the displacement vector of the object in time t to t’.
If the co-ordinate of points A and B are (x₁, y₁) and (x₂, y₂), then the position vector of the object A is r₁ = x₁i^+y₁j^ and the position vector of the object at point B is r₂ = x₂i^+y₂j^.
Therefore, displacement vector for AB will be-
∆r = r₂-r₁
Displacement Vector ∆r = (x₂-x₁)i^ + (y₂-y₁)j^