We all know that arithmetic addition arose not out of some axiomatic system, but out of the natural tendency to combine similar objects. I am satisfied with typical addition being loosely defined in this way. But when it comes to addition with other objects, like vectors, I am little bit confused. Why is that we define vector addition the way we do (i.e. a resultant vector is one that starts at the base of the first to the tip of the second)? Is this the definition of vector addition because it is the most "natural" way to "add" directed line-segments? Why does this definition happen to be so useful in physics?