Which forces are needed for the rotational motion about a fixed axis?

$A$ force $\vec{F} = 4\hat{i} + 3\hat{j} + 4\hat{k}$ is applied at the intersection point of the plane $x = 2$ and the $x$-axis. The magnitude of the torque of this force about the point $(2, 3, 4)$ is .......... . (Round off to the nearest integer)

The torque of the force $\vec{F} = (2\hat{i} - 3\hat{j} + 4\hat{k}) \text{ N}$ acting at the point $\vec{r} = (3\hat{i} + 2\hat{j} + 3\hat{k}) \text{ m}$ about the origin is:

$A$ wheel of radius $R$ with an axle of radius $R/2$ is as shown in the figure. It is free to rotate about a frictionless axis through its centre and perpendicular to the page. Three forces are exerted as shown in the figure: a force $F$ at an angle of $45^{\circ}$ to the tangent of the outer rim,a force $F$ tangential to the inner axle,and a force $2F$ tangential to the outer rim. The magnitude of the net torque acting on the system is nearly ............. $FR$.

$A$ force of $-P \hat{k}$ acts on the origin of the coordinate system. The torque about the point $(2, -3)$ is $P(a \hat{i} + b \hat{j})$. If the ratio $\frac{a}{b} = \frac{x}{2}$,find the value of $x$.

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