Question

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

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

Answer 1

The correct option is D It is zero vector

given

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

Let

$\overrightarrow{a}=\hat{i}$

$\overrightarrow{b}=\hat{j}$

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

$\hat{i}\times \hat{j}=\hat{k}$

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

$\hat{k}\times \hat{k}=0$