3D Geometry · Foot of perpendicular on line

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

\left(0, \dfrac34, \dfrac{-1}{4}\right)

, then the value of

a^2 + b^2 + \alpha^2

is equal to:

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