Let $P$ be the plane $\sqrt{3} \mathrm{x}+2 \mathrm{y}+3 \mathrm{z}=16$ and let $\mathrm{S}=\left\{\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}}: \alpha^2+\beta^2+\gamma^2=1\right.$ and the distance of $(\alpha, \beta, \gamma)$ from the plane P is $\left.\frac{7}{2}\right\}$. Let $\bar{u}, \bar{v}$ and $\bar{w}$ be three distinct vectors in $S$ such that $|\bar{u}-\bar{v}|=|\bar{v}-\bar{w}|=|\bar{w}-\bar{u}|$. Let $V$ be the volume of the parallelepiped determined by vectors $\vec{u}, \vec{v}$ and $\vec{w}$. Then the value of $\frac{80}{\sqrt{3}} \mathrm{~V}$ is