Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) be three vectors such ...

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