Vector Algebra: JEE Main 2026 Mathematics question

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