Let : \(\vec{a}=\hat{i}+2\hat{j}+3\hat{k},\vec{b}=\hat{i}−\hat{j}+2\hat{k}\) and \(\vec{c}=5\hat{i}−3\hat{j}+3\hat{k}\) …

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 there vectors. If \(\vec{r}\) is a vector such that, \(\vec{r}\times \vec{b}=\vec{c}\times \vec{b}\) and \(\vec{r}⋅\vec{a}=0,\) then \(25{\left|\vec{r}\right|}^{2}\) is equal to

[JEE Main 2023, 30 Jan (Shift 2)]