Let $\vec{\alpha }=\left(\lambda -2\right)\vec{a}+\vec{b}$ and $\vec{\beta }=\left(4\lambda -2\right)\vec{a}+3\vec{b}$ be two given vectors where vectors $\vec{a}$ and $\vec{b}$ are non-collinear. The value of $\lambda$ for which vectors $\vec{\alpha }$ and $\vec{\beta }$ are collinear, is