Screenshot_4.pngLet  be the force acting on a particle having position vector  and   be the torque of this force about the origin. Then

We know that $\vec{\tau }=\vec{r}\times\vec{f}$
$\vec{r}.\vec{\tau }=\vec{r}.\left ( \vec{r}\times \vec{f} \right )=0$
$\therefore \vec{f}.\vec{\tau}=\vec{f}.\left ( \vec{r}\times\vec{f} \right )=0$