Let $\vec a=\hat{\imath}+2\hat{\jmath}+3\hat{k}$, $\vec b=\hat{\imath}-\hat{\jmath}+2\hat{k}$ and $\vec c=5\hat{\imath}-3\hat{\jmath}+3\hat{k}$ be three 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 $25\lvert\vec r\rvert^{2}$ is equal to: