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## Homework Statement

Let 'S' be the collection of vectors [x;y;z]

in R

^{3}that satisfy the given property. Either prove that 'S' forms a subspace of R

^{3}or give a counterexample to show that it does not.

|x-y|=|y-z|

## Homework Equations

## 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.