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:

The force $\vec{F} = 7\hat{i} + 3\hat{j} - 5\hat{k}$ acts on a particle whose position vector is $\vec{r} = \hat{i} - \hat{j} + \hat{k}$. What is the torque of the given force about the origin?

$A$ person supports a book between his finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of $W$,then the person is producing a torque on the book of

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:

$A$ force $\overrightarrow{F} = (\hat{i} + 2\hat{j} + 3\hat{k}) \text{ N}$ acts at a point $\vec{r}_1 = (4\hat{i} + 3\hat{j} - \hat{k}) \text{ m}$. The magnitude of torque about the point $\vec{r}_2 = (\hat{i} + 2\hat{j} + \hat{k}) \text{ m}$ is $\sqrt{x} \text{ N-m}$. The value of $x$ is $........$

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