1. The problem statement, all variables and given/known data Let 'S' be the collection of vectors [x;y;z] in R3 that satisfy the given property. Either prove that 'S' forms a subspace of R3 or give a counterexample to show that it does not. |x-y|=|y-z| 2. Relevant equations 3. The attempt at a solution First I tested the 0 vector, and it passed that test. Now I have to test if it is closed under scalar multiplication and addition. This is where I am getting confused. I don't know if it is the absolute value signs that are confusing me, or if I am just generally unsure how to proceed. Thanks.