If $\overrightarrow{\mathrm{F}}$ is the force acting on a particle having position vector…
If $\overrightarrow{\mathrm{F}}$ is the force acting on a particle having position vector $\overrightarrow{\mathrm{r}}$ and $\vec{\tau}$ be the torque of this force about the origin, then :
$\vec{r} \cdot \vec{\tau}=0$ and $\vec{F} \cdot \vec{\tau} \neq 0$
$\overrightarrow{\mathrm{r}} \cdot \vec{\tau} \neq 0$ and $\vec{F} \cdot \vec{\tau}=0$
$\overrightarrow{\mathrm{r}} \cdot \vec{\tau}=0$ and $\vec{F} \cdot \vec{\tau}=0$
Solution
$\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}$
$\vec{\tau}$ is perpendicular to $\overrightarrow{\mathrm{r}}$ and $\vec{F}$.
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