Question

Three vectors satisfy the relation $\overrightarrow{A}.\overrightarrow{B}=0$ and $\overrightarrow{A}.\overrightarrow{C}=0$ then $\overrightarrow{A}$ is parallel to

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

Answer 1

Answer: (A)

Here $\overrightarrow{A}.B$ =$ABcos\theta$ = $ABcos90^{\circ }$ = O $\Rightarrow$ $\overrightarrow{A}\perp \overrightarrow{B}$ Similarly, $\overrightarrow{A}\perp \overrightarrow{C}\Rightarrow \overrightarrow{B}$ and $\overrightarrow{C}$ are in the same plane and $\overrightarrow{A}$ is perpendicular to them. Thus $\overrightarrow{A}||\overrightarrow{B}\times \overrightarrow{C}$