For inner product spaces, do we have $||\vec{u}-\vec{v}|| \leq ||\vec{u}||+||\vec{v}||$? 
Let $V$ be an inner product space.  Then for all $\vec{u},\vec{v} \in V$ we have $$||\vec{u}-\vec{v}|| \leq ||\vec{u}||+||\vec{v}||.$$

I know that the converse to the equation is true such that $||\vec{u}+\vec{v}||$ is less than or equal to $||\vec{u}||+||\vec{v}||$.  Is this also true?

Take the triangle inequality $\|x + y\| \le \|x\| + \|y\|$.  What happens if you do $y\leftarrow -y$?
