If \(\vec{F}\) is the force acting on a particle having position vector \(\vec{r}\) and \(\vec{\tau}\) be the torque of this force about the origin, then:

\(\vec{r}.\vec{\tau}>0\) and \(\vec{F}.\vec{\tau}<0\) \(\vec{r}.\vec{\tau}=0\) and \(\vec{F}.\vec{\tau}=0\) \(\vec{r}.\vec{\tau}=0\) and \(\vec{F}.\vec{\tau} \neq 0\) \(\vec{r}.\vec{\tau} \neq 0\) and \(\vec{F}.\vec{\tau}=0\)

\(\vec{r}.\vec{\tau}=0\) and \(\vec{F}.\vec{\tau}=0\)

\(\vec{\tau} = \vec{r} × \vec{F}\) \(\tau\) is ⊥ to both \(\vec{r}\) and \(\vec{F}\) ⇒ \(\vec{r} . \vec{\tau} = 0\) \(\vec{F}.\vec{\tau}=0\)