If F be a force acting on a particle having the position vector r and $\tau$ be the torque of this force about the origin, then

• A

  $\mathbf{r}·\tau =0\text{ and }\mathbf{F}·\mathit{\tau }=0$

• B

  $r\times \tau =0\text{ and }F\times \tau \ne 0$

• C

  $\mathbf{r}·\tau \ne 0\text{ and }\mathbf{F}·\tau \ne 0$

• D

  $\mathbf{r}\times \tau \ne 0\text{ and }\mathbf{F}\times \tau =0$