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.
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.
> line(d,[1 + 2*t,t,2+2*t],t);
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.