The figure shows three forces $\overrightarrow{F}_{1}, \overrightarrow{F}_{2}$ and $\overrightarrow{F}_{3}$ acting along the sides of an equilateral triangle. If the total torque acting at point $O$ (the center of the triangle) is zero,then the magnitude of $\overrightarrow{F}_{3}$ is:

What is the torque of the force $\vec{F} = (2\hat{i} - 3\hat{j} + 4\hat{k}) \text{ N}$ acting at the point $\vec{r} = (3\hat{i} + 2\hat{j} + 3\hat{k}) \text{ m}$ about the origin?

$A$ couple produces

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

$A$ uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face,at a height $\frac{3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (assume that the cube does not slide):

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