Let the point $A$ be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-\alpha}{3}$. If the midpoint of the line segment PA is $\left(0, \frac{3}{4}, \frac{-1}{4}\right)$, then the value of $\mathrm{a}^2+\mathrm{b}^2+\alpha^2$ is equal to :