Question

If $a$ and $b$ are two non-zero, then a vector perpendicular to the vector $(b.b)a-(a.b)b$ is?

• A. $a$
• B. $b$
• C. $a–b$
• D. $a+b$

Answer 1

The correct option is B

$b$

Explanation for the correct option:

Find the perpendicular vector of $(b.b)a-(a.b)b$:

Let $\begin{array}{rcl}\overrightarrow{c}& =& \left(\overrightarrow{b}.\overrightarrow{b}\right)\overrightarrow{a}-\left(\overrightarrow{b}.\overrightarrow{a}\right)\overrightarrow{b}\end{array}$

$\begin{array}{rcl}& =& \overrightarrow{b}\times \left(\overrightarrow{a}\times \overrightarrow{b}\right)\end{array}$

$=\overrightarrow{b}$

$\therefore$The required vector is $\overrightarrow{\mathbf{b}}$.

Hence, Option ‘B’ is Correct.