Let \(\vec a = \lambda \hat i - 9\hat j - \hat k,\;\vec b = 3\hat i + 3\hat j + \hat k\;and\;\vec c = 4\hat i + 2\hat j + \hat k\). The value of λ for which the vector \(\vec a\) is perpendicular to \(\vec b \times {\rm{\;}}\vec c\) is ________.
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