If $\overrightarrow a = 2\hat i + 2\hat j + 3\hat k,\: \overrightarrow b = − \hat i + 2\hat j + \hat k$ and $\overrightarrow c = 3\hat i + \hat j$ are such that $\overrightarrow a + λ\overrightarrow b$ is perpendicular to $\overrightarrow c$ , then find the value of $λ.$

Question

$\begin{array}{1 1}(A) \lambda=8 \\ (B) \lambda=-8 \\(C) \lambda=\large\frac{1}{8} \\(D) \lambda=-\large\frac{1}{8} \end{array}$