Question

If $\overline{a}$ is a unit vector then $\overline{a}\times (\overline{b}\times (\overline{a}\times \overline{b}\left)\right)$

• A. $(\overline{b}\times \overline{a})$
• B. $(\overline{b}.\overline{a})(\overline{b}\times \overline{a})$
• C. $(\overline{a}\times \overline{b})$
• D. $-\overline{a}.\overline{b}$

Answer 1

The correct option is B $(\overline{b}.\overline{a})(\overline{b}\times \overline{a})$

$\overline{a}\times [\overline{b}\times (\overline{a}\times \overline{b}\left)\right]=\overline{a}\times \left[\right(\overline{b}\cdot \overline{b})\overline{a}-(\overline{b}\cdot \overline{a}\left)\overline{b}\right]$

$=(\overline{b}\cdot \overline{b})(\overline{a}\times \overline{a}-(\overline{b}\cdot \overline{a}\left)\right(\overline{a}\times \overline{b})$

$=0+(\overline{b}\cdot \overline{a})(\overline{b}\times \overline{a})$ , Since $\overline{b}\times \overline{a}=-\overline{a}\times \overline{b}$

$=(\overline{b}\cdot \overline{a})(\overline{b}\times \overline{a})$