Can anyone help me make a start on showing that this set is a subspace of $R^3$? Or provide a counter example that it is not? I know that I need to show that it is closed under addition and scalar multiplication but not sure where to start. Probably quite simple.
$$(x,y,z)\in \mathbb{R}^3 ; \lvert x-y \rvert = \lvert y-z \rvert$$
Thanks!
Hint:
$|1-0|=|0-1|$ and $|-1-0|=|0-1|$