For example, you traveled from point A to point B. And if you look at your journey path, you will see that your total displacement is AB. Which depends on two points.
And if you express this displacement in vector form, it is called displacement vector. For example
That is the curved path that you have moved from point A to point B. And this displacement vector is not dependent on that path. It just depends on your initial and final position.
What is the difference between displacement and displacement vector?
You may think that displacement and displacement vector are two different concepts but no, they are both the same thing.
When a particle moves from point A to point B, you cannot express its displacement by scalars. Always expressed in vector form.
The displacement vector is represented in exactly the same way.
And it is true that if given the position vectors of two points their displacement is always called a displacement vector.
Graphical representation of a position vector
When a particle moves from point A to point B, to determine the displacement of the particle, it is necessary to know the position of both the points.
So, you cannot determine the displacement between the two points until you know the position of both the points.
In this case, to represent the displacement, the point has to be expressed in the form of a vector without being written in the coordinate system because the displacement is a vector quantity.
And when the position of a point is represented in vector form, it is called a position vector.
You can understand by looking at the image above. Here the position is according to the coordinate system of points (x,y,z). That is, the displacement of the particle along the x, y, and z axes is x, y, and z. Then the vector from the point will be
Graphical representation of a Displacement vector
The particle is moving from point A to point B in free space as shown in the figure below. Here r1 is the position vector of the initial state of the particle and r2 is the position vector of the final point. ∇r is the displacement vector of the particle.
We can write according to vector triangle law
Thus, displacement vector means that the position of the moving particle is different between the two position vectors.
And since the displacement vector here is in component form, it will have absolute value
Unit and Dimensional
The length of a straight line indicates the value of the displacement. So the unit of length is the unit of displacement. The units of displacement in different standard methods are given below
- CGS Method : Centi-Meter(cm)
- PFS Method : Foot(ft)
- SI Method : Meter(m)
And the dimension of displacement is the dimension of length i.e. L.
Zero Displacement
If the initial and end position of an object is the same, its displacement will be zero. That is, if a person starts a journey from one place and walks some distance and returns to that place again, his movement will be zero.
In this case, the distance to the object will not be but zero. And there is no direction of zero displacements.
Question and Answer
Q1. An object particle is moving in a circular path. Whose radius is two units. So what will be the displacement vector of the particle in each of the following cases?
• A(3,6)→B(5,8) : When the object moves from point A to point B, its position increases by two units along both axes. Then there will be a displacement of the object.
• A(3,6)→C(7,6) : In this case, the position of the object will not change along the y axis. Rather, there will be displacement along the x-axis.
• A(3,6)→D(5,4) : In this case, the displacement value of the particle will be equal to the displacement value of the first case. But in both cases, the direction of displacement will always be different.
Q2. A particle is moving at a constant velocity. And the graph of velocity and time is drawn below according to its trajectory. And according to this graph, you draw a graph between displacement and time.
Here the particle is moving with constant velocity. Thus, the slope of the displacement and time graph will define the constant velocity. Here the graph will be a straight line that will be inclined at a certain angle along the time axis.
Conclusion
With the help of this tutorial, you will understand what is a displacement vector! Of course this is an important concept of vectors. This concept is used when determining the displacement between two positions.
