Find the equations of the planes parallel to the plane x-2y + 2z-4 = 0, which are at a unit distance from the point (1,2, 3).
The equation of the planes parallel to the plane x −2y + 2z − 4 = 0
are of the form x-2y+2z+k=0
The distance of a plane ax+by+cz+ λ from a point (x1,y1,z1) is given by
It is given the plane x-2y+2z+k=0 at an unit distance from the point (1, 2, 3).
∴ k=0 or k=-6
The equation of the planes parallel to the plane x-2y+2z-4=0
are of x-2y+2z=0 and x-2y+2z=6