Keep the Plane always in front of the Camera.

[Xieyunchen]

[AurimasBlazulionis]

You have 2 options.

1. Make the plane as a child of the camera

2. have a script attached to the plane the looks something like this:

   public float distance;
   Public Transform cam;

   void Update () {
   transform.position = cam.position + cam.forward * distance;
   }
   Edit the distance as you wish.