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} $.