The resultant of the system in the figure is a force of $8 \ N$ parallel to the given forces,acting through point $R$. The value of $PR$ is equal to . . . . . .

$A$ 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 $\,N$)

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:

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

$A$ 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 $\vec{F} = 4\hat{i} - 3\hat{j} + 4\hat{k} \, N$ acts on a particle at a position $\vec{r} = 3\hat{i} + 2\hat{j} + 3\hat{k}$ from the origin. The torque acting on the particle is: