Vector Algebra

If \(\overrightarrow a = 2\widehat i + \widehat j + 3\widehat k\), \(\overrightarrow b = 3\widehat i + 3\widehat j + \widehat k\) and \(\overrightarrow c = {c_1}\widehat i + {c_2}\widehat j + {c_3}\widehat k\) are coplanar vectors and \(\overrightarrow a \,.\,\overrightarrow c = 5\), \(\overrightarrow b \bot \overrightarrow c\), then \(122({c_1} + {c_2} + {c_3})\) is equal to ___________.