According to my textbook:
Moment of a force = force $\times$ perpendicular distance of the line of action of the force from the fulcrum.
I don't understand why it would be that way (especially what mathematics goes behind it). Why is distance taken to be perpendicular to the direction of force when calculating torque, regardless of its direction?
For example, in this question:
The answer (given by the marking scheme) is supposedly $240$ $\text{N}$ $\times 1.2$ $\text{m}$ or $288$ $\text{Nm}$. The way I usually tackle questions like these would be to resolve the vector into its components and multiply the magnitude of its vertical vector with the distance.
How does the method used above by the marking scheme work? Is there a proof which shows it does?