Question:
Three vectors satisfy the relation $\overrightarrow{A}.\overrightarrow{B}=0$ and $\overrightarrow{A}.\overrightarrow{C}=0$ then $\overrightarrow{A}$ is parallel to
Three vectors satisfy the relation $\overrightarrow{A}.\overrightarrow{B}=0$ and $\overrightarrow{A}.\overrightarrow{C}=0$ then $\overrightarrow{A}$ is parallel to
Updated On: May 19, 2023
- $\overrightarrow{B}\times\overrightarrow{C}$
- $\overrightarrow{B}.\overrightarrow{C}$
- $\overrightarrow{C}$
- $\overrightarrow{B}$
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The Correct Option is A
Solution and Explanation
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}$
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