Let a, b, c be three vectors such that a × b =2( a × c ). If | a |=1,| b |=4,| c |=2, and the angle between b and c is 60^°, then | a · c | is equal…

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