Formula : Plane = r . (n) = d

Where r = any random point

n = normal vector of plane

d = distance of plane from origin

If two planes are parallel , then their normal vectors are same.

Therefore ,

Parallel Plane r . (2i - j + 2k) = 5

Normal vector = (2i - j + 2k)

∴ Normal vector of required plane = (2i - j + 2k)

Equation of required plane r . (2i - j + 2k) = d

In cartesian form 2x - y + 2z = d

Plane passes through point (1,1,1) therefore it will satisfy it.

2(1) - (1) + 2(1) = d

d = 2 – 1 + 2 = 3

Equation of required plane r . (2i - j + 2k) = 3