Let a, b and c be three non zero vectors such that b · c =0 and a ×( b × c )=(b - c)/2. If d be a vector such that b · d = a · b, then ( a × b ) ·( c…

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