X intercept of the plane containing the line of intersection of the planes x - 2 y + z + 2 = 0 and 3 x - y - z + 1 = 0 and also passing through ( 1 , 1 , 1 ) is

Step-by-step solution

Equation of plane passing through line of intersection of given planes is given by, x - 2 y + z + 2 + α 3 x - y - z + 1 = 0 Since, the plane passes through the point 1 ,   1 ,   1 therefore, this point will satisfy equation of plane. ⇒ 1 - 2 + 1 + 2 + α 3 - 1 - 1 + 1 = 0 ⇒ α = - 1 Then, equation of planes becomes x - 2 y + z + 2 - 1 3 x - y - z + 1 = 0 ⇒ - 2 x - y + 2 z + 1 = 0 Now, X intercept of this plane can be calculated by putting y = z = 0 , we get - 2 x + 1 = 0 &#8