$A$ force $\vec{F}$ acts on a particle with position vector $\vec{r}$. The torque $\vec{\tau}$ about the origin due to this force is given by $\vec{\tau} = \vec{r} \times \vec{F}$. Which of the following is true?

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