Given that $\vec a \cdot \vec b = 0$ and $\vec a \times \vec b = \vec 0$. What can you conclude about the vectors $\vec a$ and $\vec b?$

$\vec a \cdot \vec b = \vec 0$ and $\vec a \times \vec b = \vec 0$

$\Rightarrow (\vec a = \vec 0\;or\;\vec b = \vec 0\;or\;\vec a \bot \vec b)$ and $(\vec a = \vec 0$ or $\vec b = \vec 0$ or $\vec a||\vec b$)

$\Rightarrow$ Either $\vec a = \vec 0$ or $\vec b = \vec 0$

[ and are not valid at the same time]