Connecting an object to 2 others

In the scene view create a quad and rotate it 90 degrees in the X axis. Set the X scale to however wide you want the plane to be.

You need to make sure the pivot of the plane is at its edge, so translate it -0.5 in the Z axis, then create an empty game object (at the world origin) and parent the quad to it.

The script to control the direction of the plane is really simple

 public Transform pointA, pointB;
 public GameObject plane;

 void Update(){
     plane.transform.position = pointA.position;
     plane.transform.LookAt(pointB.position);
     plane.transform.localScale = new Vector3(1, 1, Vector3.Distance(pointA.position, pointB.position));
 }

You set the position of the plane to always be at the same position as pointA. We moved the pivot so this will align one edge with pointA. Then you use transform.LookAt to look at pointB, which will rotate around the pivot constrained to pointA.

Because the quad has a scale of 1 in Z 1 unit in scale equates to one world unit so you can use the distance between the points to work out the new scale.

Hope that helped.

Mike