Why are two vectors that are parallel equivalent? Why are two parallel vectors with the same magnitude equivalent?
Why is their start point irrelevant?
How can a vector starting at $\,(0, -10)\,$ going to $\,(10, 0)\,$ be the same as 
a vector starting at $\,(10, 10)\,$ and going to $\,(20, 20)\,$?

Components of a vector determine the length and the direction of the vector, but not it's basepoint. Therefore 2 vectors are equivalent if and only if they have the same components, but this gives the idea that any 2 parallel vectors are equal though they have different base points. To avoid this confusion, we take that all vectors are based on the origin unless stated.
