$A$ force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau$ about the origin. Choose the correct option.

• A
  $\vec r \cdot \vec \tau > 0$ and $\vec F \cdot \vec \tau < 0$
• B
  $\vec r \cdot \vec \tau = 0$ and $\vec F \cdot \vec \tau = 0$
• C
  $\vec r \cdot \vec \tau = 0$ and $\vec F \cdot \vec \tau \neq 0$
• D
  $\vec r \cdot \vec \tau \neq 0$ and $\vec F \cdot \vec \tau = 0$