If \(\overrightarrow a = 2\widehat i + 2\widehat j + 3\widehat k,\overrightarrow b = - \widehat i + 2\widehat j + \hat k \rm \ and\overrightarrow c = 3\widehat i + \widehat j\) are such that \(\overrightarrow a + γ \overrightarrow b \) is perpendicular to \(\overrightarrow c \), then determine the value of γ?
1
3
2
0
3
4
4
8