If r, a, b, c are non null vectors such that $\vec r.\vec a=\vec r.\vec b=\vec r.\vec c=0$, then $[\vec a\,\vec b\,\vec c]$

is equal to zero

Since $\vec r.\vec a= 0$, $\vec r.\vec b= 0$ and $\vec r.\vec c= 0$,  $\vec r$ must be perpendicular to all the three vectors $\vec a$, $\vec b$ and $\vec c$. Hence $\vec a$, $\vec b$ and $\vec c$ must be coplanar

$⇒= [\vec a\,\vec \,\vec c]=0$

Hence (C) is the correct answer.