Question

If $\vec {r} \cdot \vec {a} = \vec {r} \cdot \vec {b} = \vec{r} \cdot \vec{c} = 0 $ for some non-zero vector $\vec {r}$, then the value of $[\vec {a} \,\vec{b} \,\vec {c}]$ is

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

Answer 1

Answer: (D)

Given, $r\cdot a=0 $
$\Rightarrow r \bot a $
$r \cdot b =0 $
$\Rightarrow r \bot b$ and $r\cdot c=0 $
$\Rightarrow r \bot c $
$\Rightarrow a, b$ and $c$ are coplanar
$\therefore \left[a \,b\, c\right]=0$