Dear mathematician,

I need to show that:

||x-y||+||y-z||=||x-z||

if and only if

y= ax + (1-a)z with 0<=a<=1

In other words, if x,y and z are on the same line, that relation between the norms must be satisfied and the other way around.

I didn't come really far. Writing out the inproducts didn't give me any insight.

Can someone help me please? Would be great!

Cheers, Eva