Let $\vec{a}=2 \hat{i}-7 \hat{j}+5 \hat{k}, \vec{b}=\hat{i}+\hat{k}$ and $\vec{c}=\hat{i}+2 \hat{j}-3 \hat{k}$ be three given vectors. If $\overrightarrow{\mathrm{r}}$ is a vector such that $\vec{r} \times \vec{a}=\vec{c} \times \vec{a}$ and $\vec{r} \cdot \vec{b}=0$, then $|\vec{r}|$ is equal to :