Question

Vectors $\vec{A},\vec{B}$ and $\vec{C}$ are such that $\vec{A}\cdot \vec{B}=0$ and $\vec{A}\cdot \vec{C}=0$ .
Then the vector parallel to $\vec{A}$ is

• A. $\vec{A}\times \vec{B}$
• B. $\vec{B}+\vec{C}$
• C. $\vec{B}\times \vec{C}$
• D. $\vec{B}$ and $\vec{C}$

Answer 1

Answer: (C)

Vector triple product of three vectors $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$ is
$\overrightarrow{A}\times (\overrightarrow{B}\times \overrightarrow{C})=(\overrightarrow{A}\cdot \overrightarrow{C})\overrightarrow{B}-(\overrightarrow{A}\cdot \overrightarrow{B})\overrightarrow{C}$
Given : $\overrightarrow{A}\cdot \overrightarrow{B}=0,\overrightarrow{A}\cdot \overrightarrow{C}=0$
$\therefore \overrightarrow{A}\times (\overrightarrow{B}\times \overrightarrow{C})$
Thus the vector $\overrightarrow{A}$ is parallel to vector $\overrightarrow{B}\times \overrightarrow{C}$.