when we find the torque produced by a person on a vending machine, with the axis

Question

when we find the torque produced by a person on a vending machine, with the axis of rotation being the back two legs of the vending machine, for the force of the person on the vending machine they use the y distance instead of the x distance (according to the coordinate axis) when finding the distance from the axis of rotation (in my book- Etkina College Physics AP Edition section 7.7)- shouldn't it be the horizontal distance? Because it's the length of the line connecting the force to the axis that's perpendicular to the axis- right?

Explanation / Answer

Torque is given by

F*r where both are vectors as r points from axis of rotation to the point where the force is applied. Now in case of vending machine the axis passing through vertical.we apply the force on one end and move the handle during which the r vector is along the vertical axis. The result of a cross-product is mathematically a vector pointing vertically upwards.

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