The equation of plane which is passing through the
point (1, 2, 3) and which is at maximum distance
from the point $(-1,0,2)$ is

Plane is passing through the point $A(1, 2, 3)$
and is at maximum distance from the point $B(-1, 0, 2).$
So, plane is perpendicular to the line $AB.$
So, direction ratios of normal to the plane are 2, 2, 1.
Hence equation of plane is $2(x-1)+2(y-2)+1(z-3)=0$ or $2x+2y+z=9$