Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane .

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.