What is the torque of force $\vec F = 2\hat i - 3\hat j + 4\hat k$ acting at a point $\vec r = 3\hat i + 2\hat j + 3\hat k$ about the origin?

Find the torque of a force $\overrightarrow F = 2\hat i + \hat j + 4\hat k$ acting at the point $\overrightarrow r = 7\hat i + 3\hat j + \hat k$.

The torque acting on a body about the centre of mass due to the normal reaction:

$A$ 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 ............. $FR$.

$A$ rod of length $l$ is acted upon by a couple as shown in the figure. The moment of the couple is $\tau \text{ Nm}$. If the force at each end of the rod is $F$,then the magnitude of each force is (given $\sin 30^{\circ} = \cos 60^{\circ} = 0.5$):

Find the torque of a force $\vec{F} = -3\hat{i} + \hat{j} + 5\hat{k}$ acting at the point $\vec{r} = 7\hat{i} + 3\hat{j} + \hat{k}$.