The rotational effect is produced by

$A$ force $\vec{F} = (2\hat{i} - \hat{j} + 3\hat{k}) \text{ N}$ is acting at a point $(-1, 2, -3) \text{ m}$. Find its torque about the origin.

$A$ force $\vec{F} = 5\hat{i} + 2\hat{j} - 5\hat{k}$ acts on a particle whose position vector is $\vec{r} = \hat{i} - 2\hat{j} + \hat{k}$. What is the torque about the origin?

$A$ force $F = 2.0\,N$ acts on a particle $P$ in the $xz-$ plane. The force $F$ is parallel to the $x-$ axis. The particle $P$ (as shown in the figure) is at a distance $3\,m$ from the origin,and the line joining $P$ with the origin makes an angle of $30^\circ$ with the $x-$ axis. The magnitude of the torque on $P$ with respect to the origin $O$ (in $N-m$) is:

$A$ rod of mass $1 \ kg$ is kept on a frictionless table and is acted upon by $2$ forces as shown. We want to replace these $2$ forces by a single force so that the effect on the rod is the same. At what distance $x$ (in $m$) from the center $C$ of the rod should we apply this single force?

When a force of $6.0 \, N$ is exerted at $30^{\circ}$ to a wrench at a distance of $8 \, cm$ from the nut,it is just able to loosen the nut. What force $F$ would be sufficient to loosen it,if it acts perpendicularly to the wrench at $16 \, cm$ from the nut (in $, N$)?