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 \ha…

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 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 \(25|\vec{r}|^2\) is equal to

[JEE Main 2023, 31 Jan (Shift 2)]