Does a vector have a location in space? Will it fluctuate with time?  Can two equivalent vectors x and y at various locations in space fundamentally have indistinguishable physical effects? Give cases in support of your answer.
Does a vector have a location in space? Will it fluctuate with time?  Can two equivalent vectors x and y at various locations in space fundamentally have indistinguishable physical effects? Give cases in support of your answer.

Ans:

No, Yes and No.

In space, a vector has no defined place. The reason for this is that when a vector displaces in such a way that its direction and magnitude do not change, it remains invariant. A position vector, on the other hand, has a distinct place in space.

A vector evolves over time. For example, the velocity vector of a ball moving at a constant speed changes over time.

The physical effect of two equivalent vectors located at distinct points in space is not the same. Two comparable forces acting at distinct spots on a body, for example, will cause the body to spin, but the combination will not provide the same turning effect.