For the rod AB to be in equilibrium while suspended by strings OA and OB, it must hang vertically due to the gravitational force acting on it. The tension in the strings must balance the weight of the rod, ensuring that the net force is zero. This condition implies that the vectors representing the tensions in the strings and the weight of the rod are coplanar. Therefore, the plane formed by points O, A, and B must be vertical. The equilibrium condition confirms that the configuration of the strings and the rod maintains a vertical alignment.