Vector Algebra

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