I understand that you want to set the angle between XY as 120 degree while keeping Z-axis perpendicular to XY plane. This can be achieved by performing coordinate transformation as given bellow:
% Generate a 3D coordinate system
figure;
quiver3(0, 0, 0, 1, 0, 0, 'r', 'LineWidth', 2); % X axis (red)
hold on;
quiver3(0, 0, 0, 0, 1, 0, 'g', 'LineWidth', 2); % Y axis (green)
quiver3(0, 0, 0, 0, 0, 1, 'b', 'LineWidth', 2); % Z axis (blue)
axis equal;
% Apply rotation transformation
angle = 120; % Angle in degrees
rotationMatrix = [cosd(angle) -sind(angle) 0; sind(angle) cosd(angle) 0; 0 0 1];
% Apply the rotation to the coordinate system
newXAxis = rotationMatrix * [1; 0; 0];
newYAxis = rotationMatrix * [0; 1; 0];
newZAxis = rotationMatrix * [0; 0; 1];
% Plot the rotated coordinate system
quiver3(0, 0, 0, newXAxis(1), newXAxis(2), newXAxis(3), 'r--', 'LineWidth', 2); % Rotated X axis (dashed red)
quiver3(0, 0, 0, newYAxis(1), newYAxis(2), newYAxis(3), 'g--', 'LineWidth', 2); % Rotated Y axis (dashed green)
quiver3(0, 0, 0, newZAxis(1), newZAxis(2), newZAxis(3), 'b--', 'LineWidth', 2); % Z axis (blue)
The rotated coordinate system is plotted using dashed lines. You can adjust the ‘angle’ variable to set the desired angle between XY axis. You may read further on ‘quiver3’ here: https://in.mathworks.com/help/matlab/ref/quiver3.html
