Which component of torque is responsible for rotation about the $Z$-axis?

$A$ 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 $x$.

$A$ 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)

$A$ force $\vec{F} = (2\hat{i} - \hat{j} + 3\hat{k}) \text{ N}$ is acting at a point $(-1, 2, -3) \text{ m}$. Find its torque about the origin.

$A$ door is hinged at one end and is free to rotate about a vertical axis (figure). Does its weight cause any torque about this axis? Give a reason for your answer.

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.