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 (1) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} = 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} \neq 0$ (2) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} \neq 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} = 0$ (3) $\vec{r} \cdot \vec{T} \neq 0$ and $\vec{F} \cdot \vec{T} \neq 0$ (4) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} = 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} = 0$
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\\
(1) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} = 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} \neq 0$\\
(2) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} \neq 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} = 0$\\
(3) $\vec{r} \cdot \vec{T} \neq 0$ and $\vec{F} \cdot \vec{T} \neq 0$\\
(4) $\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{T}} = 0$ and $\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{T}} = 0$