What does torque measure in terms of producing rotational motion?

The torque of force $\vec F = -2\hat i + 2\hat j + 3\hat k$ acting on a point $\vec r = \hat i - 2\hat j + \hat k$ about the origin will be:

Four equal and parallel forces are acting on a rod (as shown in the figure) at distances of $20 \, cm, 40 \, cm, 60 \, cm$,and $80 \, cm$ respectively from one end of the rod. Under the influence of these forces,the rod -

$A$ wheel of radius $R$ with an axle of radius $R/2$ is as shown in the figure. It is free to rotate about a frictionless axis through its centre and perpendicular to the page. Three forces are exerted as shown in the figure: a force $F$ at an angle of $45^{\circ}$ to the tangent of the outer rim,a force $F$ tangential to the inner axle,and a force $2F$ tangential to the outer rim. The magnitude of the net torque acting on the system is nearly ............. $FR$.

$A$ body of mass $10 \, kg$ is hanging at rest with the help of a rope wrapped around a cylinder of diameter $0.2 \, m$. The torque applied about the horizontal axis of the cylinder is ....... $N-m$.

Find the torque about the origin when a force of $3 \hat{j} \text{ N}$ acts on a particle whose position vector is $2 \hat{k} \text{ m}$.