Position and Displacement vector

A position vector is a vector that defines the location of a point in coordinate space. The formula we use to find the position vector from point A to point B is AB = (xk+1 – xk, yk+1 – yk). The position vector is a three-dimensional vector that plots the position of an object within three dimensions. The Displacement vector is the vector that describes the movement of a person from one place to another. The object’s displacement will be denoted by the straight line from point A to point B. In contrast, denoting the direction of the displacement vector, we always take from the direction of starting point to the ending point.

Position and Displacement vector

What is a position vector?

A position vector is a vector that defines the location of a point in coordinate space. It is a mathematical representation of the location of a point on a surface in 3-D space. It is an essential tool used in many applications of computer graphics, for example, computer graphics for graphics, animation, and video games. The position vector is a three-dimensional vector that plots the position of an object within three dimensions and is used to describe any position in space. In addition to describing the position of an object in space, a position vector also describes the shape of the object.

Position Vector Formula

The formula we use to get the position vector from point A to point B is AB = (xk+1 – xk, yk+1 – yk). The AB represents the position vector that starts from point A to B. Similarly, if we want to the find the position vector from point B to point A is BA: BA = (xk – xk+1, yk – yk+1)

How To Find the Position Vector?

Let two points A = (x1, y1) and B = (x2, y2). Now we have to find the position vector from point A to B.

To get the position vector, now we need to subtract the components of point A from Point B: AB = (x2 – x1, y2 – y1) = (x2 – x1) i + (y2 – y1) j

Position vector diagram

The position vector is a vector that takes a point on a plane and transforms it into the position of the object it represents. Position vectors are a tool used to figure out the position of a location on a map. The position vector is based on the assumption that the location is in the centre of the map. The position vector might also be based on a grid, which can be used to figure out the position of anything on the map.

What is a Displacement vector?

The Displacement vector is the vector that describes the movement of a person from one place to another. It is derived from the square root of the negative distance between two points and is the direction of movement of that person. The Displacement vector shows more clearly the direction of movement of a person than their actual distance from the two points. The displacement vector in physics is one of the key concepts used to explain the motion of a point moving in time. It explains the difference between the forces that cause a point to move and the forces that cause a point to stay still. 

Displacement vector Formula

The displacement vector is a vector that describes the position of a point in time. It is a vector entirely independent of the physical laws that govern it. The displacement vector is the difference between the position of the point and the position of the point at the time it was last seen. 

To calculate the displacement vector, we have the formula:

     Displacement vector formula s = sf – si

       s = displacement, si = initial position, sf = final position

How to find displacement vector:

We will understand this concept with the help of a displacement vector diagram. 

Conclusion

If we want to find the position vector from point B to point A, it is BA: BA = (xk – xk+1, yk – yk+1). The position vector is a vector that takes a point on a plane and transforms it into the position of the object it represents. The magnitude of the position vector is directly proportional to the distance of the point from the object’s centre. The displacements and positions are represented by the vectors: x = (x1, x2, x3), y = (y1, y2, y3), and z = (z1, z2, z3). The displacement vector is the main direction of displacement for any object, but it is often used to describe the direction of displacement for physical objects, such as a sound wave, a light beam, a plane, and the Earth’s surface