Answer :

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


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