Question

If $\overrightarrow{x}.\overrightarrow{a}=0,\overrightarrow{x}.\overrightarrow{b}=0 $ for some non-zero vectors $\overrightarrow{x} $ , then $[\overrightarrow{a}\,\overrightarrow{b} \,\overrightarrow{c} ]=0 $, is

• A. true
• B. false
• C. cannot say anything
• D. none of these.

Answer 1

Answer: (A)

Since $\vec{x}$ is $\bot$ to $\vec{a}$, $\vec{b}$, $\vec{c}$
$\therefore \vec{a}$, $\vec{b}$, $\vec{c}$ are coplanar.
$\therefore \left[\vec{a}\,\vec{b}\,\vec{c}\right]=0$