Vector Algebra

Let \(\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow b\) and \(\overrightarrow c = \widehat j - \widehat k\) be three vectors such that \(\overrightarrow a \times \overrightarrow b = \overrightarrow c\) and \(\overrightarrow a \,.\,\overrightarrow b = 1\). If the length of projection vector of the vector \(\overrightarrow b\) on the vector \(\overrightarrow a \times \overrightarrow c\) is l, then the value of 3l² is equal to _____________.