Q. If $\overrightarrow{\mathbf{r}} \bullet \overrightarrow{\mathbf{a}} = 0,\overrightarrow{\mathbf{r}} \bullet \overrightarrow{\mathbf{b}} = 0\ and\ \overrightarrow{\mathbf{r}} \bullet \overrightarrow{\mathbf{c}} = 0\$ for some non-zero vector $\overrightarrow{\mathbf{r}}.$ Then, the value of $\lbrack\overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{c}}\rbrack$ is
A) 0
B) $\frac{1}{2}$
C) 1
D) 2
Explanation
(a)
The given condition mean that $\overrightarrow{\mathbf{r}}$ is perpendicular to all three vectors $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}$ and $\overrightarrow{\mathbf{c}}$. This is possible only if they are coplanar.
$\therefore\ \ \left\lbrack \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{c}} \right\rbrack = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.