Question

If $\overline{r}\cdot \overline{a}=\overline{r}\cdot \overline{b}=\overline{r}\cdot \overline{c}$ for some non-zero vector $\overline{r}$ then the value of $\left[\overline{a}\overline{b}\overline{c}\right]$ is

• A. $3$
• B. $0$
• C. $2$
• D. None of these

Answer 1

Answer: (B)

$0$

Since $=\overline{r}\cdot \overline{a}=\overline{r}\cdot \overline{b}=\overline{r}\cdot \overline{c}=0$
$=\therefore \overline{a},\overline{b}$ and $\overline{c}=0$ are coplanar $(\because \overline{r}\ne \overline{0})$
$\therefore \left[\overline{a}\overline{b}\overline{c}\right]=0$