Question

If three vectors satisfy the relation $\overrightarrow{A}.\overrightarrow{B}=0$ and $\overrightarrow{A}.\overrightarrow{C}=0$ , then $\overrightarrow{A}$ can be parallel to

• A. $\overrightarrow{C}$
• B. $\overrightarrow{B}$
• C. $\overrightarrow{B}\times \overrightarrow{C}$
• D. $\overrightarrow{B}.\overrightarrow{C}$

Answer 1

The correct option is C $\overrightarrow{B}\times \overrightarrow{C}$

$\overrightarrow{A}.\overrightarrow{B}=0\Rightarrow \overrightarrow{A}\perp \overrightarrow{B}$
and, $\overrightarrow{A}.\overrightarrow{C}=0\Rightarrow \overrightarrow{A}\perp \overrightarrow{C}$
Also, $\overrightarrow{B}\times \overrightarrow{C}$ is perpendicular to both $\overrightarrow{B}and\overrightarrow{C}$
$Thus,\overrightarrow{A}||(\overrightarrow{B}\times \overrightarrow{C})$