Force times distance is called "Work" for the purposes of physics.
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Work is defined as the dot product of force times distance, or W = F * d = Fd cos (theta) where theta is the angle in between the force and distance vectors (if you are doing two dimensions). In three dimensions, use the standard definition for the dot product (using the component form of the vectors).
Force times distance equals work.
Yes.
Yes and no. It's the dot product, but not the cross product.
Torque is calculated by multiplying a force by the distance from the fulcrum at which it acts.