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If \( \overrightarrow a,\overrightarrow b \: and \overrightarrow c \)are three mutually perpendicular vectors of equal magnitude, prove that the angle which \( (\overrightarrow a+\overrightarrow b+\overrightarrow c)\) makes with any of the vectors \( \overrightarrow a, \overrightarrow b \: or \overrightarrow c\) is \( \cos^{-1}\large\frac{1}{\sqrt3}.\)

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