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

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

Which factors should be considered for the calculation of torque,and which should not?

$A$ force $F = 2.0\,N$ acts on a particle $P$ in the $xz-$ plane. The force $F$ is parallel to the $x-$ axis. The particle $P$ (as shown in the figure) is at a distance $3\,m$ from the origin,and the line joining $P$ with the origin makes an angle of $30^\circ$ with the $x-$ axis. The magnitude of the torque on $P$ with respect to the origin $O$ (in $N-m$) is:

Give the formula for the moment of a couple.

How is the direction of torque determined?