If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is

The correct option is 2x + 5y – 6z + k = 0.

To understand why this is the correct answer, let us analyze the general equation of a plane in three-dimensional space.
The general equation of a plane is given by:
a x + b y + c z + d = 0
where the coefficients a, b, and c represent the components of the normal vector n → = ( a , b , c ) which is perpendicular to the plane.

For any two planes to be parallel, their normal vectors must be parallel (or identical). This means that the coefficients of x, y, and z in the equation of the parallel plane must be proportional to those of the given plane.
Therefore, the equation of a plane parallel to a x + b y + c z + d = 0 can be written by keeping the x, y, and z terms the same, and only changing the constant term d to an arbitrary constant k:
a x + b y + c z + k = 0

Given the equation of the plane:
2 x + 5 y − 6 z + 3 = 0
Here, the coefficients are a=2, b=5, and c=−6.
Substituting these values, the general equation of a parallel plane is:
2 x + 5 y − 6 z + k = 0
where k is any real constant.