If $\bar{a}$ and $\bar{b}$ are two vectors such that $|\bar{a}|=|\bar{b}|=\sqrt{6}$ and $\bar{a} \cdot \bar{b}=-1$ then $|\bar{a} \times \bar{b}| \sin (\bar{a}, \bar{b})=$

• A

  $\left(|\bar{a}|^2-1\right)\left(|\bar{b}|^2+1\right)$
• B

  $\frac{1}{6}$
• Correct answer
  C

  $\left(|\bar{a}|^2-1\right)\left(1+\frac{1}{|\bar{b}|^2}\right)$
• D

  $\frac{\sqrt{35}}{6}$

Hence, the correct answer is option: 'C'.