Given a set of Euclidean Vectors with $N$ dimensions, whose distance from a Euclidean Vector, $R$, is less than some Constant, $C$.
Can the max distance between any two vectors in the set be determined?
I have been searching for some sort of proof or rule but I can't seem to fine one, when I picture a sphere with $R$ at the center, I believe the max distance would be $2C$. However I am unsure if this is true for dimensions greater than $3$.