Originally Posted by

**Chris L T521** $\displaystyle \begin{aligned}\left|\left|u\right|\right|=...\\ &\iff\left<u,u\right>=\left<v,v\right>\\ &\iff\left<u,u\right>-\left<v,v\right>=0\\ &\iff\left<u,u\right>+\left<u,v\right>-\left<u,v\right>-\left<v,v\right>=0\\ &\iff\left<u,u\right>+\left<v,u\right>+\left<u,-v\right>+\left<v,-v\right>=0\\ &\iff\left<u+v,u\right>+\left<u+v,-v\right>=0\\&\iff\left<u+v,u-v\right>=0\qquad\square\end{aligned}$

Does this make sense? Some steps are skipped -- see if you can fill them in.