Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three non zero vectors such that \(\vec{b} \cdot \vec{c}=0\) and \(\vec{a} \…

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

[JEE Main 2023, 25 Jan (Shift 1)]