If the lines x-1 2 = y+1 3 = z-1 4 and x-2 1 = y+m 2 = z-2 1 intersect each other, then the value of m is....

Step-by-step solution

Let the given lines be L₁ and L₂ . Any point on L₁ is given by (2r₁ + 1, 3r₁ - 1, 4r₁ + 1) . Any point on L₂ is given by (r₂ + 2, 2r₂ - m, r₂ + 2) . For the lines to intersect, these points must coincide for some values of r₁ and r₂ . Equating the x , y , and z coordinates: 2r₁ + 1 = r₂ + 2 2r₁ - r₂ = 1 3r₁ - 1 = 2r₂ - m 3r₁ - 2r₂ = 1 - m 4r₁ + 1 = r₂ + 2 4r₁ - r₂ = 1 Solving the first and third equations: 4r₁ - r₂ = 1 2r₁ - r₂ = 1 Subtracting the two equations gives 2r₁ = 0 r₁ = 0 . Substituting r₁ = 0 in 2r₁ - r₂