What is the vector quantity that describes the shortest path between two points

displacement

Explanation:

1) While the distance covered is a scalar, displacement is a vector.

2) Displacement, the shortest path between two points, is calculated by subtracting the initial position from final position. So what happens in the middle does not count.

3) Displacement is a vector as it includes information about the direction of the motion.

4) For example: suppose the starting is in the position (0, 10) and the end is in the position (5, 20), the displacement is the vector:

          displacement: (5i - 0i, 20j - 10j) = (5i, 10j)

On the other hand, if the starting position is (5,20) and the final position is (0,10), the displacment is the vector:

          displacement = (0i - 5i, 10j - 20j) = (-5i - 10j)

In the given examples both vectors (displacements) have the same magnitude but opposite direction.