Given that $\overrightarrow a . \overrightarrow b = 0$ and $\overrightarrow a$ x $\overrightarrow b = \overrightarrow 0$ What can you conclude about the vectors $\overrightarrow a$ and $\overrightarrow b$?

Question

$\begin{array}{1 1} (A) \overrightarrow a\:and\:\overrightarrow b \;are\; parallel \\ (B) \overrightarrow a\:and\:\overrightarrow b \;are\; \perp \\ (C) |\overrightarrow a|=0\:or\:|\overrightarrow b|= 0 \\ (D) |\overrightarrow a|=|\overrightarrow b|\end{array}$