Consider the lines \( L_{1}: {x-1} = {y-2} = {z} \) and \( L_{2}: {x-2} = {y} = {z-1} \). Let the feet of the perpendiculars from the point \( P(5,1,-3) \) on the lines \( L_{1} \) and \( L_{2} \) be \( Q \) and \( R \) respectively. If the area of the triangle \( PQR \) is \( A \), then \( 4A^{2} \) is equal to:
