Drawing a line perpendicular to a line on a plane whose normal is known

I have two vector(Vector3) positions of a line on a plane whose normal vector is known .What I am trying to do is draw a line perpendicular to this line on the same plane. Suppose end1 and end2 are two vectors representing the ends of the original line What I am trying right now :

                 var line1 = end1 + ( (end2-end1)* 1 );
          var rotatedLine = Quaternion.AngleAxis( 90, anchor.transform.rotation*Vector3.up ) * end1;
                    //Debug.DrawLine(end2, rotatedLine, Color.blue);
                    var newLine1 = Instantiate(line );
                    LineRenderer lr2 = newLine1.GetComponent<LineRenderer>();
                    lr2.SetPosition(0,end1);
                    lr2.SetPosition(1,rotatedLine);

If the line belongs to the plane, it means this line is perpendicular to the normal.

So you are trying to find a new line perpendicular to the 1st line and to the normal.

You are looking for the cross product

Vector3 planeNormal = ... ;
Vector3 lineOnThePlane = ... ;
Vector3 result = Vector3.Cross( planeNormal.normalized, lineOnThePlane.normalized ) ;