Q 11-03-006JEE MainAIEEE 2003Medium
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
Answer: (D) $\vec{r}\cdot\vec{\tau} = 0$ and $\vec{F}\cdot\vec{\tau} = 0$
The torque about the origin is $\vec{\tau} = \vec{r} \times \vec{F}$.
A cross product is perpendicular to both of the vectors that form it. So $\vec{\tau}$ is perpendicular to $\vec{r}$ and to $\vec{F}$, and both dot products vanish:
$$\vec{r}\cdot\vec{\tau} = 0, \qquad \vec{F}\cdot\vec{\tau} = 0$$
Solution by Sreeraj P, M.Sc Physics