# Find the equation

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

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