The point of intersection of the lines x+13=y+35=z+57 and x−21=y−43=z−65 is

Let x+13=y+35=z+57=λ so that a general point on it is P(3λ−1,5λ−3,7λ−5) let x−21=y−43=z−65=μ So that general point on it isQ(μ+2,3μ+4,5μ+6) . The two lines intersect P and Q coincide ∴3λ−1=μ+2,5λ−3=3μ+4,7λ−5=5μ+6 Solving first two equations, we get λ=12,μ=−32 These values satisfy the third equation. hence, coordinates of point  of intersection are (12,−12,−32)