Let : \(\vec{a}=\overset{^}{i}+2\overset{^}{j}+3\overset{^}{k},\vec{b}=\overset{^}{i}−\overset{^}{j}+2\overset{^}{k}\) a…

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