Question

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two non-zero vectors, then a vector perpendicular to the vector $(\overrightarrow{b}.\overrightarrow{b})\overrightarrow{a}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{b}$ is

• A. $\overrightarrow{a}$
• B. $\overrightarrow{b}$
• C. $\overrightarrow{a}-\overrightarrow{b}$
• D. $\overrightarrow{a}+\overrightarrow{b}$

Answer 1

Answer: (B)

Let $\vec{c}=\left(\vec{b}.\vec{b}\right)\vec{a}-\left(\vec{b}.\vec{a}\right)\vec{b}=\vec{b}\times \left(\vec{a}\times \vec{b}\right)$
Since $\vec{b}.\vec{c}=0$
$\therefore \vec{b}$ is the reqd. vector.