Find the equations of the plane parallel to the plane `x-2y+2z-3=0\ ` and which are at a unit distance from the point (1, 1, 1).

Explanation

The equation of the plane parallel to the given plane is


`x-2y+2z_k=0 ldots ldots (1)`

It is given that plan `(1)` is at a distance of 1 unit from `(1,1,1)`

`Rightarrow (|1-2+2+k|)/sqrt(1^2 + (-2)^2 + 2^2) = 1`

`Rightarrow |1+k|/3 = 1`

`Rightarrow |1 + k| = 3`

`Rightarrow 1+k=3 ; 1+k=-3`

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