Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) be three non zero vectors such that \( \vec{b} \cdot \vec{c}=0 \) and \( \vec{a} \times(\vec{b} \times \vec{c})=\frac{\vec{b}-\vec{c}}{2} \). If \( \vec{d} \) be a vector such that \( \vec{b} \cdot \vec{d}=\vec{a} \cdot \vec{b} \), then \( (\vec{a} \times \vec{b}) \cdot(\vec{c} \times \vec{d}) \) is equal to
