Let \( \vec{F} \) be the force acting on a particle having position vector \( \vec{r} \) and \( ...

Let \( \vec{F} \) be the force acting on a particle having position vector \( \vec{r} \) and \( \vec{\tau} \) be the torque of this force about the origin. Then
[AIEEE 2003; Similar CBSE PMT 2009]
(a) \( \vec{r} \cdot \vec{\tau}=0 \) and \( \vec{F} \cdot \vec{\tau}=0 \)
(b) \( \vec{r} \cdot \vec{\tau}=0 \) and \( \vec{F} \cdot \vec{\tau} \neq 0 \)
(c) \( \vec{r} \cdot \vec{\tau} \neq 0 \) and \( \vec{F} \cdot \vec{\tau}=0 \)
(d) \( \vec{r} \cdot \vec{\tau} \neq 0 \) and \( \vec{F} \cdot \vec{\tau} \neq 0 \)