Plane with line rotation/transformation

Hello,

I have set of 3 points which creates a plane. In addition I have a set of two points which create a line. I would like to transform/rotate my plane with line in the way that a new plane will lay on xy plane (z=0). Below, I present my script in Matlab. It seems that it working. I have a good angle between a new plane and a new position of line. However, if I check an angle between my reference plane XY 2x-y=1 the angle is differ.I know they are shifted on z axis but I think the angle should stay the same. Am I right or I miss something? What I am doing wrong? Thank you for any help.

% xy plane z=0

p1 = [2 3];  % Point 1 for the plane
p2 = [1 1];  % Point 2 for the plane

syms x y z
M1 = [x y 1; p1(1) p1(2) 1; p2(1) p2(2) 1]; % Matrix to solve

P1 = vpa(det(M1));   % equation of the plane

D1 = double(subs(P1, {x, y, z}, {0, 0, 0}));        % D coeefitient of the plane equation
A1 = double(subs(P1, {x, y, z}, {1, 0, 0}))-D1;      % A coeefitient of the plane equation
B1 = double(subs(P1, {x, y, z}, {0, 1, 0}))-D1;      % B coeefitient of the plane equation
C1 = double(subs(P1, {x, y, z}, {0, 0, 1}))-D1;      % C coeefitient of the plane equation

format short e

P1 = [-37.77 -58.85 -34.67];  % Point 1 for the plane
P2 = [27.53 -61.54 -28.18];  % Point 2 for the plane
P3 = [-58.91 15.29 -50.52];  % Point 3 for the plane

plane_old=[P1; P2; P3]; 

w = cross(plane_old(2,:)-plane_old(1,:),plane_old(3,:)-plane_old(1,:));
w = w/norm(w);
R = [null(w),w.'];

if det(R)<0, R(:,1:2) = R(:,2:-1:1); end

plane_new = plane_old*R;

P1 = plane_new(1,1:3);
P2 = plane_new(2,1:3);
P3 = plane_new(3,1:3);

syms x y z

M = [x y z 1; P1(1) P1(2) P1(3) 1; P2(1) P2(2) P2(3) 1; P3(1) P3(2) P3(3) 1]; % Matrix to solve

% M = [x y 1; P1(1) P1(2) 1; P2(1) P2(2) 1] % Matrix to solve

P = vpa(det(M));   % equation of the plane

D = double(subs(P, {x, y, z}, {0, 0, 0}));      % D coeefitient of the plane equation
A = double(subs(P, {x, y, z}, {1, 0, 0}))-D;     % A coeefitient of the plane equation
B = double(subs(P, {x, y, z}, {0, 1, 0}))-D;     % B coeefitient of the plane equation
C = double(subs(P, {x, y, z}, {0, 0, 1}))-D;     % C coeefitient of the plane equation

Ap = [-19.29 5.57 -15.67];  % Up point
A0 = [ -1.6452e+001 -6.1967e+000 -9.5058e+000]; % Down point

Ap_new = Ap*R;

A0_new = A0*R;

syms t
line = vpa(A0_new + t*(Ap_new-A0_new)) % line equation

a = Ap_new(1)-A0_new(1); % a coeefitient of the line equation
b = Ap_new(2)-A0_new(2); % a coeefitient of the line equation
c = Ap_new(3)-A0_new(3); % a coeefitient of the line equation

angle1 = asin(abs(A*a+B*b+C*c)/(sqrt(A^2+B^2+C^2)*sqrt(a^2+b^2+c^2)))*180/pi % angle between line and plane
angle1 = asin(abs(A1*a+B1*b+C1*c)/(sqrt(A1^2+B1^2+C1^2)*sqrt(a^2+b^2+c^2)))*180/pi % angle between line and plane xy

[X,Y] = meshgrid(-50:.1:50, -50:1:50); % net of the points to draw plane
Z = ((-A.*X-B.*Y-D)./C);
surf(X,Y,Z,'EdgeColor','none','FaceColor','red');
hold on
alpha(0.3)
grid on

Z1 = zeros(101,1001);
surf(X,Y,Z1,'EdgeColor','none','FaceColor','green');
alpha(0.3)
t = linspace(-10,10,10);
plot3(A0_new(1)+t*(Ap_new(1)-A0_new(1)),A0_new(2)+t*(Ap_new(2)-A0_new(2)),A0_new(3)+t*(Ap_new(3)-A0_new(3)),'LineWidth',2,'Color','blue');
plot3(Ap_new(1), Ap_new(2), Ap_new(3),'.','MarkerSize',30,'Color','red');
plot3(A0_new(1), A0_new(2), A0_new(3),'.','MarkerSize',30,'Color','m');

[Sreeja Banerjee]

Hi Kamil, Can you please clarify what you mean by "if I check an angle between my reference plane XY 2x-y=1 the angle is differ.". Also it will be helpful if you can give an example on what values you expect and what you are getting.