Answer
If $(u+v) $ and $(u-v)$ are orthogonal this implies $(u+v) \cdot (u-v)=0$, then the vectors $u$ and $v$ must have the same length.
Work Step by Step
$(u+v) $ and $(u-v)$ are orthogonal when $(u+v) \cdot (u-v)=0$
$u \cdot u-u.v+v.u-v.v=0$
$u.u-v.v=0$
Since,$u.u=|u|^2$
Thus, $|u|^2=|v|^2$
Hence, it has proved that if $(u+v) $ and $(u-v)$ are orthogonal this implies that $(u+v) \cdot (u-v)=0$; thus the vectors $u$ and $v$ must have the same length.
