Question

If $\overline{a}$ and $\overline{b}$ are unit vectors, then the vector $(\overline{a}+\overline{b})\times (\overline{a}\times \overline{b})$ is parallel to the vector

• A. $\overline{a}-\overline{b}$
• B. $\overline{a}+\overline{b}$
• C. $2\overline{a}-\overline{b}$
• D. $2\overline{a}+\overline{b}$

Answer 1

Answer: (A)

$\overline{a}-\overline{b}$

$(\overline{a}+\overline{b})\times (\overline{a}\times \overline{b})$
$=\overline{a}\left(\right(\overline{a}+\overline{b}).\overline{b})-\overline{b}\left(\right(\overline{a}+\overline{b}).\overline{a})$
$=\overline{a}(\overline{a}.\overline{b}+\overline{b}.\overline{b})-\overline{b}(\overline{a}.\overline{a}+\overline{b}.\overline{a})$
$=\overline{a}(ab+1)-\overline{b}(1+ab)$
$=(\overline{a}\overline{b}+1)(\overline{a}-\overline{b})$