A subspace of R³ : the set of all length-3 vectors [x; y; z] such that x + y + z = 0 where x, y, and z are real-valued numbers

The Axiom: (u + v) + w = u + (v + w)

Does this axiom hold with regards to the vector space, or does it not hold. Please show all steps when proving or disproving, thank you!