If the lines x 1 = y 2 = z 3 , x - k 3 = y - 3 - 1 = z - 4 h and 2 x + 1 3 = y - 1 1 = z - 2 1 are concurrent, then the value of 2 h - 3 k is equal to

Step-by-step solution

Any general point on the line x 1 = y 2 = z 3 is λ , 2 λ , 3 λ Any general point on the line x + 1 2 3 = y - 1 2 = z - 2 2 is 3 μ - 1 2 , 2 μ + 1,2 μ + 2 If these two lines are intersecting, then λ 3 μ - 1 2 = 2 λ 2 μ + 1 = 3 λ 2 μ + 2 ⇒ μ = 1 2 So, the point of intersection is 1,2 , 3 and it must satisfy the third line. 1 - k 3 = 2 - 3 - 1 = 3 - 4 h 1 - k 3 = 1 = - 1 h ⇒ k = - 2 , h = - 1