## Position Vector and Displacement – Class 11 | Chapter – 4 | Physics Short Notes Series PDF for NEET & JEE

Position Vector and Displacement: In physics, position vector and displacement are two important concepts that describe the motion of objects in space. A position vector is a vector that points from the origin of a coordinate system to the position of an object in space. Displacement is the change in position of an object over time. It is a vector quantity that describes the straight-line distance and direction between the initial and final positions of an object.

## Position Vector and Displacement

Position Vector

A position vector is a vector that points from the origin of a coordinate system to the position of an object in space. It is represented by the symbol “r” and is expressed in terms of its x, y, and z components. For example, if an object is located at position (2, 3, 4) in a Cartesian coordinate system, its position vector would be r = 2i + 3j + 4k, where i, j, and k are the unit vectors in the x, y, and z directions, respectively. The magnitude of the position vector represents the distance between the object and the origin of the coordinate system.

Position Displacement

Displacement is a vector quantity that describes the change in position of an object over a given period of time. It is represented by the symbol “Δr” (delta r) and is expressed in terms of its x, y, and z components. For example, if an object moves from position (2, 3, 4) to position (6, 5, 8) in a Cartesian coordinate system, its displacement would be Δr = (6-2)i + (5-3)j + (8-4)k = 4i + 2j + 4k. The magnitude of the displacement vector represents the shortest distance between the initial and final positions of the object.

## Difference between Position Vector and Displacement

The main difference between position vector and displacement is that position vector describes the position of an object relative to the origin of a coordinate system, while displacement describes the change in position of an object over time.

More specifically, here are some key differences between position vector and displacement:

• Definition: A position vector is a vector that points from the origin of a coordinate system to the position of an object in space, while displacement is a vector that describes the change in position of an object over time.
• Representation: Position vector is usually represented by the symbol “r” and is expressed in terms of its x, y, and z components, while displacement is represented by the symbol “Δr” (delta r) and is expressed in terms of its x, y, and z components as well.
• Origin: The position vector always points from the origin of a coordinate system to the position of an object, while the displacement vector points from the initial position of an object to its final position.
• Magnitude: The magnitude of the position vector represents the distance between the object and the origin of the coordinate system, while the magnitude of the displacement vector represents the shortest distance between the initial and final positions of the object.
• Direction: Position vector does not have a direction since it only describes the position of an object, while displacement vector has both magnitude and direction that depends on the direction of the movement of the object.

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