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.

The rotational motion of a body is caused by:

The rotational effect is produced by

$A$ force $\overrightarrow{F} = 4\hat{i} - 5\hat{j} + 3\hat{k}$ acts at a point $\overrightarrow{r_1} = \hat{i} + 2\hat{j} + 3\hat{k}$. The torque about the point $\overrightarrow{r_2} = 3\hat{i} - 2\hat{j} - 3\hat{k}$ is:

Three forces $F, 2F$ and $3F$ act on a rod $AB$ which is pivoted at $A$. The anticlockwise moments of forces $F, 2F$ and $3F$ about the pivot $A$ are respectively:

$A$ 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 $\tau_z$?