Why do r and F need to be perpendicular for two angles to give the same torque?

[Ronnin]

Unless r and F are perpendicular, there are always two angles between their directions that give the same torque for given magnitudes of r and F. Explain why?

Perhaps I cannot visualize the question, but I cannot see how this can be. As the force moves to the perpendicular position the torque increases. Am I missing something?

 

[neutrino]

Use the definition of torque. If one angle between the p.v and force vector is theta, what about the other?

Edit: I guess this holds only for the magnitude of the torque.

 

[Zeno's Paradox]

\tau = rF \sin \theta

sin \theta = \sin (\pi - \theta)​

 

[Ronnin]

I guess I figured that would put the angle outside of between the two angles.