Explain the difference between scalar and vector quantities using distance and displacement as examples

Scalar quantities are quantities that are fully described by a magnitude (or numerical value) alone. Vector quantities are quantities that are fully described by both a magnitude and a direction.

Let's use distance and displacement as examples to illustrate the difference:

1. Distance: This is a scalar quantity. It refers to "how much ground an object has covered" during its motion. For example, if you walk around a 400m track, your distance is 400m, regardless of your starting and ending point or the path you took. It only has magnitude and no direction.

2. Displacement: This is a vector quantity. It refers to "how far out of place an object is"; it is the object's overall change in position. If you walk around a 400m track and end up at your starting point, your displacement is 0m, because your change in position is zero. If you walk in a straight line from the starting point to a point 100m away, your displacement is 100m in the direction of that point. It has both magnitude (100m) and direction (towards the point).

So, the main difference between scalar and vector quantities is that scalar quantities have only magnitude, while vector quantities have both magnitude and direction.