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

The Correct Option is A

Here $\overrightarrow{A} .{B}$ =$AB\, cos \theta$ = $AB\, cos 90^\circ$ = 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}$