Let: \( \vec{a}=\hat{i}+2\hat{j}+3\hat{k} \), \( \vec{b}=\hat{i}-\hat{j}+2\hat{k} \) and \( \vec{c}=5\hat{i}-3\hat{j}+3\hat{k} \) be vectors. If \( \vec{r} \) is a vector such that, \( \vec{r}\times\vec{b}=\vec{c}\times\vec{b} \) and \( \vec{r}\cdot\vec{a}=0 \), then \( 25|\vec{r}|^{2} \) is equal to:
