Proving that the vector norm definition of distance satisfies the distance triangle inequality – math.stackexchange.com

I know that, for $\vec{u},\vec{v},\vec{w}\in V$ where $V$ is an inner product space, the distance between $\vec{u}$ and $\vec{w}$ is given by the norm $d\left( \vec{u},\vec{w}\right)=\left| ...