Vector Algebra

Let a vector \(\overrightarrow c\) be coplanar with the vectors \(\overrightarrow a = - \widehat i + \widehat j + \widehat k\) and \(\overrightarrow b = 2\widehat i + \widehat j - \widehat k\). If the vector \(\overrightarrow c\) also satisfies the conditions \(\overrightarrow c \,.\,\left[ {\left( {\overrightarrow a + \overrightarrow b } \right) \times \left( {\overrightarrow a \times \overrightarrow b } \right)} \right] = - 42\) and \(\left( {\overrightarrow c \times \left( {\overrightarrow a - \overrightarrow b } \right)} \right)\,.\,\widehat k = 3\), then the value of \(|\overrightarrow c {|^2}\) is equal to :