The required plane is parallel to , so required plane and the given plane must have the same normal vector.
Vector normal to the plane is
The required plane is passing through a given point
(a, b, c), so can write the position vector of the point as
Now, the equation of the required plane is given by,
(x - a) + (y - b) + (z - c)=0
x + y + z - (a + b + c)=0
x + y + z = a + b + c
Hence, the equation of the plane passing through (a, b, c) and parallel to the plane is i.e. (in vector form), or, in general form x + y + z = a + b + c.
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