Let: a = i +2 j +3 k, b = i - j +2 k and c =5 i -3 j +3 k be there vectors. If r is a vector such that, r × b = c × b and r · a =0, then 25| r |^2 is…

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