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Solve this following

Question:

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear and

$(\overrightarrow{\mathrm{a}}, \times \overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{c}}=\frac{1}{3}|\overrightarrow{\mathrm{b}}||\overrightarrow{\mathrm{c}}| \overrightarrow{\mathrm{a}}$. If $\theta$ is the angle between vectors $\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$, then a value of $\sin \theta$ is :

  1. $\frac{2}{3}$

  2. $\frac{-2 \sqrt{3}}{3}$

  3. $\frac{2 \sqrt{2}}{3}$

  4. $\frac{-\sqrt{2}}{3}$


Correct Option: , 3

Solution:

 

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