Mathematics Question from JEE Main 2026 · 23 January, Shift 2

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