The torque of a force $\overrightarrow{F} = -3\hat{i} + \hat{j} + 5\hat{k}$ acting at the point $\overrightarrow{r} = 7\hat{i} + 3\hat{j} + \hat{k}$ is:

Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$ and $\vec{T}$ be the torque of this force about the origin. Then:

$A$ 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 $\tau_z$?

$A$ force $\vec{F}$ acts on a particle with position vector $\vec{r}$. The torque $\vec{\tau}$ about the origin due to this force is given by $\vec{\tau} = \vec{r} \times \vec{F}$. Which of the following is true?

Which type of motion exists due to the moment of force (couple)?

$A$ force of $40\, N$ acts on a point $B$ at the end of an $L$-shaped object,as shown in the figure. The angle $\theta$ that will produce the maximum moment of the force about point $A$ is given by: