A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown. A force F is applied at the other end, at an angle $\theta $ to the rod. If F were to be applied perpendicular to the rod, at what distance from the axis should it be applied in order to produce the same torque?<image 1>
['L sin $\\theta $', 'L cos $\\theta $', 'L', 'L tan $\\theta $']