Vector Algebra

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