### Position Vector

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.

### Displacement Vector

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^

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