I'll try to keep it clear: I want to use a background in Blender and for that I use a plane that I want always to fit the camera viewport.
I wanted to do it cleanly, so I put a plane at the same location and orientation as the camera and now I want to move the plane along the camera axis and change it's scale to always fit the viewport (what you can see in the camera view).
I used cos and sin with the FOV of the camera to move the plane but I didn't have anything correct (not so good at math...) and I don't get how I can have the plane to always fit the viewport (fill it entirely).