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Let \( \overrightarrow a = \hat i + \hat j,\overrightarrow b = \hat i - \hat j \: and \: \overrightarrow c = \hat i + 2\hat j + 3\hat k,\) if \( n \) is unit vector such that \( \overrightarrow a.\overrightarrow n=0 \: and \: \overrightarrow b.\overrightarrow n=0,\) then show that \( \overrightarrow c.\overrightarrow n=3.\)

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