## Displacement and its vector nature

### Definition of Displacement

Displacement is the shortest distance between two positions.

### How displacement is a vector quantity?

Geometrically, displacement is the vector obtained by subtracting the initial position of an object from the its final position.

Consider the figure. Let a body is at the point ‘A’ at some instant of time. OA = ri is its initial position vector. Let after some time, the body moves to point ‘B’and its final position is represented by the position vector OB = rf. The change in position is = Δr = rfri. Then Δr is called the displacement of the body after time Δt.

So to find the displacement of a body, this is easy to draw the position vectors of the body at initial and final positions. Then draw a vector between the tips of these vectors pointing to the final position side of the body. This gives the displacement of the body both in magnitude and direction.

### Displacement and Distance

It should be noted that displacement and distance is not always the same thing. These are, in fact, different physical quantities. Distance is the trajectory of the total journey of the moving body, whereas, displacement is the shortest distance between the initial and final positions, not necessarily traversed by the body!