If $\overrightarrow {\rm{r}} \cdot \overrightarrow {\rm{a}} = 0,$ $\overrightarrow {\rm{r}} \cdot \overrightarrow {\rm{b}} = 0$ and $\overrightarrow {\rm{r}} \cdot \overrightarrow {\rm{c}} = 0$ for some non-zero vector $\overrightarrow {\rm{r}} ,$ then the value of $\overrightarrow {\rm{a}} \cdot (\overrightarrow {\rm{b}} \times \overrightarrow {\rm{c}} )$ is..............
Since, $\overrightarrow {\rm{r}}$ is a non-zero vector. So, we can say that
$\overrightarrow {\rm{a}} ,\overrightarrow {\rm{b}}$ and $\overrightarrow {\rm{c}}$
are in a same plane.
$\therefore$ $\overrightarrow {\rm{a}} \cdot (\overrightarrow {\rm{b}} \times \overrightarrow {\rm{c}} ) = 0$
[since, angle between $\overrightarrow {\rm{a}} ,\overrightarrow {\rm{b}}$ and $\overrightarrow {\rm{c}}$ are zero i.e., $\theta = 0]$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.