Let $\overrightarrow{\mathrm{a}} = 2\hat{i} - \hat{j} + 3\hat{k}$, $\overrightarrow{\mathrm{b}} = 3\hat{i} - 5\hat{j} + \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be a vector such that $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}} = \overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}}$ and $(\vec{a} + \vec{c}) \cdot (\vec{b} + \vec{c}) = 168$. Then the maximum value of $|\vec{c}|^2$ is:\\
(1) 462\\
(2) 77\\
(3) 154\\
(4) 308