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Let  be the force acting on a particle having position

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