Let the line \( L : \dfrac{x-1}{2} = \dfrac{y+1}{-1} = \dfrac{z-3}{1} \) intersect the plane \( 2x + y + 3z = 16 \) at the point \( P \). Let the point \( Q \) be the foot of perpendicular from the point \( R(1,-1,-3) \) on the line \( L \). If \( \alpha \) is the area of triangle \( PQR \), then \( \alpha^{2} \) is equal to _____.
