Q. Three vectors $\overrightarrow{A},\ \overrightarrow{B}$ and $\overrightarrow{C}$ satisfy the relation $\overrightarrow{A} \bullet \ \overrightarrow{B} = 0$ and $\overrightarrow{A} \bullet \ \overrightarrow{C} = 0$. If $\overrightarrow{B}$ and $\overrightarrow{C}$ are not lying in the same plane then $\overrightarrow{A}$ is parallel to
A) $\overrightarrow{B}$
B) $\overrightarrow{C}$
C) $\overrightarrow{B} \times \overrightarrow{C}$
D) $\overrightarrow{B} \bullet \overrightarrow{C}$
Explanation
(c) As, $\overrightarrow{A} \bullet \ \overrightarrow{B} = 0$ so $\overrightarrow{A}$ is perpendicular to $\overrightarrow{B}.$ Also $\overrightarrow{A}.\overrightarrow{C} = 0$ means $\overrightarrow{A}$ is perpendicular to $\overrightarrow{C}.$ Since $\overrightarrow{B} \times \overrightarrow{C}$ is perpendicular to $\overrightarrow{B}$ and $\overrightarrow{C}$ , so $\overrightarrow{A}$ parallel to $\overrightarrow{B} \times \overrightarrow{C}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.