Which is the vector quantity that describes the shortest path between two points?
Displacement is a vector quantity that describes the shortest path between two points!
The vector quantity that describes the shortest path between two points is known as the displacement vector. To understand why, let's first define what a vector is and then explain how the displacement vector relates to the shortest path.
A vector is a mathematical object that has both magnitude (size or length) and direction. It is represented graphically as an arrow, with the length of the arrow representing the magnitude and the orientation of the arrow representing the direction.
In physics, displacement is defined as the change in position of an object. It is a vector quantity because it has both magnitude (the distance between the initial and final positions) and direction (the straight line joining the initial and final positions).
Now, let's consider the shortest path between two points. By definition, the shortest path is the direct path, also called a straight line, between the two points. This path represents the displacement between the initial and final positions. Since displacement is a vector quantity, the shortest path is described by the displacement vector.
To calculate the displacement vector, you need to determine the magnitude and direction. The magnitude can be found using distance formula, which is the straight-line distance between the two points. The direction is given by the angle between the line joining the two points and a reference axis (such as the positive x-axis).
So, in conclusion, the displacement vector is the vector quantity that describes the shortest path between two points, and it represents the magnitude and direction of the straight-line distance between the initial and final positions.