$A$ force of $(2\hat i - 4\hat j + 2\hat k) \ N$ acts at a point $(3\hat i + 2\hat j - 4\hat k) \ m$ from the origin. The magnitude of torque is ......... $N-m$.

$A$ force $F\,\hat{k}$ acts at the origin $O$ of a coordinate system. What is the torque about the point $(1, -1, 0)$?

The coordinates of a particle with respect to origin in a given reference frame is $(1, 1, 1) \ m$. If a force of $\vec{F} = \hat{i} - \hat{j} + \hat{k} \ N$ acts on the particle,then the magnitude of the torque (with respect to origin) in the $z$-direction is . . . . . . .

$A$ 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):

If $\vec{F} = (5 \hat{i} - 10 \hat{j}) \text{ N}$ and $\vec{r} = (4 \hat{i} - 3 \hat{j}) \text{ m}$,then the torque $\vec{\tau}$ acting on the object will be:

$A$ door $1.2 \,m$ wide requires a force of $1 \,N$ to be applied perpendicularly at the free end to open or close it. The perpendicular force required at a point $0.2 \,m$ distant from the hinges for opening or closing the door is: (in $\,N$)