A line with direction ratios \( 1,-1,2 \) intersects the lines \( \dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z+1}{3} \) and \( \dfrac{x+1}{-1}=\dfrac{y-2}{1}=\dfrac{z}{4} \) at the points \( P \) and \( Q \), respectively. If the length of the line segment \( PQ \) is \( a \), then \( 225a^{2} \) is equal to:
