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

Let \(\vec{a}=2\overset{^}{i}−5\overset{^}{j}+5\overset{^}{k}\) and \(\vec{b}=\overset{^}{i}−\overset{^}{j}+3\overset{^}{k}\). If \(\vec{c}\) is a vector such that \(2(\vec{a} \times \vec{c})+3(\vec{b} \times \vec{c})=\overrightarrow{0}\) and \((\vec{a}-\vec{b}) \cdot \vec{c}=-97\), then \(|\vec{c} \times \hat{k}|^2\) is equal to

[JEE Main 2026, 24 Jan (Shift 2)]