Question

Three vectors $\overset{\rightarrow}{a},\overset{\rightarrow}{b}$and $\overset{\rightarrow}{c}$ satisfy the relation $\overset{\rightarrow}{a}.\overset{\rightarrow}{b} = 0$ and $\overset{\rightarrow}{a}.\overset{\rightarrow}{c} = 0.$ The vector $\overset{\rightarrow}{a}$ is parallel to

• A. $\overset{\rightarrow}{b}$
• B. $\overset{\rightarrow}{c}$
• C. $\overset{\rightarrow}{b}.\overset{\rightarrow}{c}$
• D. $\overset{\rightarrow}{b} \times \overset{\rightarrow}{c}$

Answer 1

Answer: (D)

$\overset{\rightarrow}{b} \times \overset{\rightarrow}{c}$

Answer 2

$\overrightarrow{a}.\overrightarrow{b} = 0$i.e. $\overrightarrow{a}$and $\overrightarrow{b}$will be perpendicular to each other

$\overrightarrow{a}.\overrightarrow{c} = 0$i.e. $\overrightarrow{a}$and $\overrightarrow{c}$will be perpendicular to each other

$\overrightarrow{b} \times \overrightarrow{c}$will be a vector perpendicular to both $\overrightarrow{b}$ and$\overrightarrow{c}$

So $\overrightarrow{a}$is parallel to $\overrightarrow{b} \times \overrightarrow{c}$