Answer
Sum of two vectors having same length will always be orthogonal to their difference.
Work Step by Step
Let us consider two vectors $v_1$ and $v_2$.
and $(v_1+v_2) \cdot (v_1-v_2)=v_1 \cdot v_1+v_2 \cdot v_1-v_1 \cdot v_2 -v_2 \cdot v_2$
Therefore,
$v_1 \cdot v_1+v_2 \cdot v_1-v_1 \cdot v_2 -v_2 \cdot v_2=|v_1|^2-|v_2|^2$
To get the answer equal to zero we will have to consider $|v_1|^2 =|v_2|^2$. This can be only possible when both have the same length.
This implies that $|v_1|^2-|v_2|^2=|v_1|^2-|v_1|^2=0$
we conclude that the sum of two vectors having same length is always orthogonal to their difference.
