Vector Algebra

If the vectors \(\overrightarrow a = \lambda \widehat i + \mu \widehat j + 4\widehat k\), \(\overrightarrow b = - 2\widehat i + 4\widehat j - 2\widehat k\) and \(\overrightarrow c = 2\widehat i + 3\widehat j + \widehat k\) are coplanar and the projection of \(\overrightarrow a\) on the vector \(\overrightarrow b\) is \(\sqrt {54}\) units, then the sum of all possible values of \(\lambda + \mu\) is equal to :