If (2 α+1, α^2-3 α, (α-1)/2) is the image of (α, 2 α, 1) in the line (x-2)/3=(y-1)/2=z/1, then the possible value(s) of α is (are)

If $\displaystyle \left(2 \alpha+1, \alpha^2-3 \alpha, \frac{\alpha-1}{2}\right)$ is the image of $\displaystyle (\alpha, 2 \alpha, 1)$ in the line $\displaystyle \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}$, then the possible value(s) of $\displaystyle \alpha$ is (are)