Vector Addition in Euclidean Space I am reading Rudin's Principles of Mathematical Analysis, and I came across something in the proof that I don't quite understand. 
Let $x$ and $z$ be vectors in $\mathbb R^k$ for some $k \geq 3$ and $r >0 $ is a real number. Suppose $| z - x | = r$. Then this means that $z = x + ru$ for some unit vector $u$. 
I am struggling to see why this is true. Can someone help me clarify this? 

Let $r = u/\|u\|$.  This will do the job.
