If the plane P passes through the intersection of two mutually perpendicular planes 2 x + k y - 5 z = 1 and 3 k x - k y + z = 5 , k < 3 and intercepts a unit length on positive x -axis, then the intercept made by the plane P on the y -axis is

Step-by-step solution

Given the plane P passes through the intersection of two mutually perpendicular planes 2 x + k y - 5 z = 1 and 3 k x - k y + z = 5 , k < 3 Since planes are mutually perpendicular Then, 2 3 k + k - k + - 5 1 = 0 ⇒ 6 k - k 2 - 5 = 0 ⇒ k = 1 , 5 But k < 3 So k = 1 Now plane passing through these planes will be, 2 x + y - 5 z - 1 + λ 3 x - y + z - 5 = 0 ⇒ x 5 λ + 1 2 + 3 λ + y 5 λ + 1 1 - λ + z 5 λ + 1 λ - 5 = 1 Given 5 λ + 1 2 + 3 λ = 1 ⇒ &#9