Let V be a vector space, and let d be a metric on V satisfying $\displaystyle d(x,y) = d(x-y,0) $and$\displaystyle d(ax,ay) = |a|d(x,y) $for every $\displaystyle x,y \in V$ and every scalar a. Show that $\displaystyle ||x||=d(x,0)$ defines a norm on V (that has d as it standard metric). Give an example of a metric on the vector space R that fails to be associated with a norm in this way.