Position and Displacement Vectors

Introduction

A quantity that contains both the direction as well as the magnitude is known as a vector. For instance, let’s consider position and velocity. For describing the position and the motion of a particle that is moving in a plane, these types of quantities are very useful. The triangle law and the law of parallelogram addition are followed by all the vectors. 

Kinematics plays a very important role in describing the difference between displacement vector and position vector, defining the position and the displacement vectors. One of the most crucial concepts of physics is displacement vectors.

Position vector

For finding the location of one object relative to another object, the position vectors are used. These vectors generally terminate at any other arbitrary point and begin at the origin. Therefore, for determining the position of a specific point with respect to its origin the position vectors are used. 

Position Vector: Definition

Mainly a straight line that has one end fixed to a body and the other end attached to a moving point for describing the position of the point relative to the body is known as a position vector. The position vector will change in direction or length or both directions as well as length when the point moves. 

Any point that either concerns arbitrary reference points, like the origin or the position, is referred to as the Position Vector. From the origin of that vector towards any given point is the direction of the position vector. 

Position Vector: Example

For instance, let’s say we have two vectors, P and Q, 

The position vector of p = (2,4) 

The position vector of q = (3,5)

Now, let’s say an origin O has come. 

Here, a particle that moves from point P to point Q will be considered. And as we have understood above, starting from the origin to the point where the particle is located, this way, we can define the position vector of a particle.

We got, 

For a position vector of a particle that is at point, P is the vector OP. 

Similarly, a position vector of a particle that is at point Q is the vector OQ. 

For finding the position vector, firstly it is very important to determine the coordinates of a particular point. 

Now, let’s say we are considering two points, A and B.

In which, 

• A = (x1, y1) 
• B = (x2, y2)

Following, we will find the position vector of AB.

Now, for determining this position vector, it would require us to subtract the corresponding components of A from B: 

Therefore, AB = (x2 – x1, y2 – y1) = (x2 – x1)i  + (y2 – y1) j

Position Vector Formula

For finding the position vector of any x-y place, firstly, it is required for us to know the coordinates of the point. 

Let’s assume two points, R and S.

So, (x1, y1) and (x2, y2) are the coordinates.

Now, similarly, for determining the position vector, it’s required for us to subtract the corresponding components of R from S:

RS = (x2 – x1, y2 – y1) = (x2 – x1) i+ (y2 – y1)j

So, the position vector of RS:

• At point R, it begins
• And at point S, it terminates.  

Definition of the Displacement Vectors

One of the most crucial concepts of mathematics is displacement vectors. An object’s distance travelled and the direction of an object in a straight line is represented by the displacement vectors. However, in physics, we frequently used the word ‘displacement vectors’ for determining the acceleration, speed, and distance of an object travelling. 

Example of the Displacement Vector

For instance, Sneha travelled from Point A to point B. By looking at the journey path we will notice the total displacement is AB. In vector form, the displacement is known as the displacement vector. 

Conclusion

A quantity that contains both the direction as well as the magnitude is known as Vector. For instance, let’s say position and velocity. Kinematics plays a very important role in describing the difference between displacement vector and position vector. Mainly a straight line that has one end fixed to a body and the other end is attached to a moving point for describing the position of the point relative to the body is known as a position vector. 

An object’s distance travelled and the direction of an object in a straight line is represented by the displacement vectors. The triangle law and the law of parallelogram addition are followed by all the vectors. The position vector will change in direction or length or both directions as well as length when the point moves. In vector form, the displacement is known as the displacement vector.