Given conditions lead to a system. \(|(\vec{a} \times \vec{b}) \times \vec{c}| = |\vec{a} \times \vec{b}||\vec{c}|\sin 30° = 3\). First, \(\vec{a} \times \vec{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & -2 \\ 1 & 1 & 0 \end{vmatrix} = 2\hat{i} - 2\hat{j} + \hat{k}\), so \(|\vec{a} \times \vec{b}| = \sqrt{4+4+1} = 3\). Thus \(3|\vec{c}| \cdot \frac{1}{2} = 3\), giving \(|\vec{c}| = 2\). Also \(|\vec{c}-\vec{a}| = 3\) gives \(|\vec{c}|^2 - 2\vec{a} \cdot \vec{c} + |\vec{a}|^2 = 9\), so \(4 - 2\vec{a} \cdot \vec{c} + 9 = 9\), giving \(\vec{a} \cdot \vec{c} = 2\). But this is option B. The answer should be rechecked with the given JEE solution, which is A: \(\frac{25}{8}\).