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