Vector Algebra: JEE Main 2026 Mathematics question

Let $\vec a, \vec b, \vec c$ be three vectors such that $\vec a\times\vec b=2(\vec a\times\vec c)$. If $|\vec a|=1$, $|\vec b|=4$, $|\vec c|=2$, and the angle between $\vec b$ and $\vec c$ is $60^\circ$, then $|\vec a\cdot\vec c|$ is equal to