$A$ couple produces

The moment of the force,$\overrightarrow{F} = 4\hat{i} + 5\hat{j} - 6\hat{k}$ at point $(2, 0, -3)$,about the point $(2, -2, -2)$,is given by

$A$ solid cone hangs from a frictionless pivot at the origin $O$,as shown. If $\hat{i}$,$\hat{j}$,and $\hat{k}$ are unit vectors,and $a, b$,and $c$ are positive constants,which of the following forces $\vec{F}$ applied to the rim of the cone at a point $P$ results in a torque $\vec{\tau}$ on the cone with a negative $z$-component $\tau_z$?

For a particle moving in a circular path under the influence of a central force,the angular momentum remains constant because .......

The torque due to the force $\vec{F} = (2 \hat{i} + \hat{j} + 2 \hat{k})$ about the origin,acting on a particle whose position vector is $\vec{r} = (\hat{i} + \hat{j} + \hat{k})$,is:

$A$ force of $-F \hat{k}$ acts on $O$,the origin of the coordinate system. The torque about the point $(1, -1)$ is