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 what can you say about [\(\vec{a}, \vec{b}, \vec{c}\)] ?

is equal to zero

Since \(\vec{r}.\vec{a} = 0 ; \vec{r}.\vec{b} = 0 ; \vec{r}.\vec{c} = 0\) , \(\vec{r}\) 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.

[\(\vec{a}, \vec{b}, \vec{c}\)] = 0