Show that $| \overrightarrow a | \overrightarrow b + | \overrightarrow b | \overrightarrow a$ is perpendicular to $| \overrightarrow a | \overrightarrow b - | \overrightarrow b | \overrightarrow a$, for any two nonzero vectors $\overrightarrow a$ and $\overrightarrow b$.

Question

$\begin{array}{1 1}(A) \overrightarrow a.\overrightarrow b=0 \\(B) \overrightarrow a=\overrightarrow b \\ (C) \overrightarrow a.\overrightarrow b=1 \\(D) None \;of\; the\; above \end{array}$