Let a, b and c be three vectors such that | a |=√ 3,| b |=5, b · c =10 and the angle between b and c is (π)/3. If a is perpendicular to the vector b…

Let $\displaystyle \vec{a}, \vec{b}$ and $\displaystyle \vec{c}$ be three vectors such that $\displaystyle |\overrightarrow{\mathrm{a}}|=\sqrt{3},|\overrightarrow{\mathrm{~b}}|=5, \overrightarrow{\mathrm{~b}} \cdot \overrightarrow{\mathrm{c}}=10$ and the angle between $\displaystyle \vec{b}$ and $\displaystyle \vec{c}$ is $\displaystyle \frac{\pi}{3}$. If $\displaystyle \vec{a}$ is perpendicular to the vector $\displaystyle \vec{b} \times \vec{c}$, then $\displaystyle |\overrightarrow{\mathrm{a}} \times(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})|$ is equal to \_\_\_\_.