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LetÂ  be the force acting on a particle having position

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

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We know that $\vec{\tau }=\vec{r}\times\vec{f}$

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

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

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