If vectros $ \overrightarrow a = 2\hat i + 2\hat j +3\hat k , \overrightarrow b = -\hat i + 2\hat j +\hat k \: and \: \overrightarrow c = 3\hat i + \hat j $ are such that $( \overrightarrow a +\lambda \overrightarrow b)$ is perpendicular to $( \overrightarrow c )$, then find the value of $( \lambda )$

Question

$\begin{array}{1 1}\text{a. 8} \\ \text{b. 6} \\ \text{c. 9} \\ \text{d. 5} \end{array} $