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