We know that equation of plane passing through the intersection of planes a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c₂z + d₂ = 0 is given by

(a₁x + b₁y + c₁z + d₁) + k(a₂x + b₂y + c₂z + d₂) = 0

So, equation of plane passing through the intersection of planes

x – 2y + z – 1 = 0 and 2x + y + z – 8 = 0 is

(x – 2y + z – 1) + k(2x + y + z – 8) = 0 ……(1)

⇒ x(1 + 2k) + y(– 2 + k) + z(1 + k) + (– 1 – 8k) = 0

We know that line is parallel to plane a₂x + b₂y + c₂z + d₂ = 0 if a₁a₂ + b₁b₂ + c₁c₂ = 0

Given the plane is parallel to line with direction ratios 1,2,1

1×(1 + 2k) + 2×(– 2 + k) + 1×(1 + k) = 0

⇒ 1 + 2k – 4 + 2k + 1 + k = 0

⇒ k =

Putting the value of k in equation (1)

⇒

⇒

⇒ 9x – 8y + 7z – 21 = 0

We know that the distance (D) of point (x₁,y₁,z₁) from plane ax + by + cz – d = 0 is given by

o, distance of point (1,1,1) from plane (1) is

⇒

⇒

⇒

Taking the mod value we have