If $\overline{\mathrm{r}}. \overline{\mathrm{a}} = \overline{\mathrm{r}}.\overline{\mathrm{b}} =\overline{\mathrm{r}}. \overline{\mathrm{c}} = 0$ where $\overline{\mathrm{a}},\overline{\mathrm{b}},\overline{\mathrm{c}}$ are non - coplanar then

$$\begin{gathered} \overline{\mathrm{r}}. \overline{\mathrm{a}} =0= \overline{\mathrm{r}}.\overline{\mathrm{b}} =\overline{\mathrm{r}}. \overline{\mathrm{c}} \\ \overline{\mathrm{r}}\perp \overline{\mathrm{a}}, \overline{\mathrm{r}}\perp \overline{\mathrm{b}}, \overline{\mathrm{r}}\perp \overline{\mathrm{c}} \Rightarrow \overline{\mathrm{r}} \left|\right|\overline{ \mathrm{a}}\times \overline{\mathrm{b}} \\ \left(\mathrm{or}\right) \overline{\mathrm{r}} \left|\right| \overline{\mathrm{b}}\times \overline{\mathrm{c}} \\ \left(\mathrm{or}\right) \overline{\mathrm{r}} \left|\right| \overline{\mathrm{c}}\times \overline{\mathrm{a}} \end{gathered}$$

$\Rightarrow \overline{\mathrm{r}}=\overline{0}$  becomes $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are non coplaner.