Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) be three non zero vectors such that \( \vec{b}\!\cdot\!\vec{c} = 0 \) and \( \vec{a} \times (\vec{b} \times \vec{c}) = \dfrac{\vec{b} - \vec{c}}{2} \). 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:
