Let \( \vec{a} = 9\hat{i} - 13\hat{j} + 25\hat{k} \), \( \vec{b} = 3\hat{i} + 7\hat{j} - 13\hat{k} \) and \( \vec{c} = 17\hat{i} - 2\hat{j} + \hat{k} \) be three given vectors. If \( \vec{r} \) is a vector such that \( \vec{r} \times \vec{a} = (\vec{b} + \vec{c}) \times \vec{a} \) and \( \vec{r} \cdot (\vec{b} - \vec{c}) = 0 \), then \( \dfrac{\left|593 \vec{r} + 67 \vec{a}\right|^2}{(593)^2} \) is equal to ______.
