Question: Equation of a plane (2)

Write the equation for the plane P contains the straight line 

d: x = 2 + t, y = t, z = 2 + 2t,

so that, the distance  from point A(2; 5; 3)  to P is maximum.

My idea.

Let K and H  be projection of the point A on the plane P and the line d, respectively. We have AK <= AH. Thus, distance from A to P reaches the maximum value if and only H coincides with K, and then P through the point K and having AH as its normal vector. 

This is my code.

  > with(geom3d);

> point(A,2,5,3);
                               
> line(d,[1 + 2*t,t,2+2*t],t);
                               
> coordinates(projection(H,A,d));
                          
> dsegment(AH,A,H);
                                
> plane(P,[H,AH]);
                            
> Equation(P,[x,y,z]);

Note that P is the plane containing the straight line d and perpendicular to the plane created by point A and the line d.

Please comment about my code. Thank you very much.