I have an plane object which is the target for Camera.LookAt. I want to rotate the plane in a way that always the planar region faces the camera. Help??
Just have your plane transform LookAt the camera.
First, this is easiest if the natural rotation of the plane is vertical. You can use the CreatePlane script to create a vertical plane. If you use the build-in plane, I suggest you have an empty game object with rotation(0,0,0) with the build-in plane as a child with a rotation that faces the camera. If you camera is looking at positive āZā (default camera setup in a new scene), then you can use (-90,0,0) for the plane rotation.
As for the rotation script, you can put these lines in Update() of a script attached to the plane (or on the empty game object if you go with the build-in plane solution):
var v3 = transform.position - Camera.main.transform.position;
transform.rotation = Quaternion.LookRotation(v3);