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Find the shortest distance between the lines $ \overrightarrow r = \hat i + 2\hat j + 3\hat k + \lambda(2\hat i + 3\hat j + 4 \hat k) \: and \: \overrightarrow r = 2\hat i + 4\hat j + 5\hat k + \mu(3\hat i + 4\hat j + 5 \hat k). $

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