Let $\overrightarrow{\mathrm{a}}=6 \hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{\mathrm{b}}=\hat{i}+\hat{j}$. If $\overrightarrow{\mathrm{c}}$ is a is vector such that $$|\overrightarrow{\mathrm{c}}| \geq 6, \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=6|\overrightarrow{\mathrm{c}}|,|\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}}|=2 \sqrt{2}$$ and the angle between $\vec{a} \times \vec{b}$ and $\vec{c}$ is $60^{\circ}$, then $|(\vec{a} \times \vec{b}) \times \vec{c}|$ is equal to:

1. A $\frac{3}{2} \sqrt{6}$
2. B $\frac{9}{2}(6-\sqrt{6})$
3. C $\frac{9}{2}(6+\sqrt{6})$ Correct answer
4. D $\frac{3}{2} \sqrt{3}$