Let α =(λ-2) a + b and β =(4 λ-2) a +3 b be two given vectors where vectors a and b are non-collinear. The value of λ for which vectors α and β are…

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