Vector displacement around a closed loop

[zezima1]

My book says that the total vector displacement around a closed loop is zero. Is this a general thing for every type of closed loop?
If so, should this be obvious?

 

[DryRun]

Well, it just means that you're back to the point where you started. So, the vector displacement is indeed zero. It's like moving from point A on the circumference of a circle and rotating around until you reach point A again. So, you had a certain scalar displacement (the value of the circumference of the circle) but the vector displacement is zero.

To answer your questions, yes, the rule applies to any kind of closed loop, which includes any dimensions, i think.

 

[HallsofIvy]

In a Euclidean space, moving a vector around a closed loop will return it to exactly the same vector. In a more general space, moving a vector around a closed loop will return to the same point but the vector may not be pointing in the same direction.

 

[DryRun]

In a Euclidean space, moving a vector around a closed loop will return it to exactly the same vector. In a more general space, moving a vector around a closed loop will return to the same point but the vector may not be pointing in the same direction.

Thanks for this clarification, HallsofIvy.