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If \( \overrightarrow a, \overrightarrow b \) and \( \overrightarrow c \) are three unit vectors such that \( \overrightarrow a.\overrightarrow b = \overrightarrow a. \overrightarrow c = 0\) and angle between \( \overrightarrow b \: and \: \overrightarrow c \) is \( \large\frac{\pi}{6}, \) prove that \( \overrightarrow a = \pm\: 2 ( \overrightarrow b\) x \( \overrightarrow c ) \).

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