Final answer:
The torque of the force of 20 N applied at position vector r = (4.0i - 2.0j) m about the origin is 80 N·m.
Step-by-step explanation:
The torque of a force about the origin can be found using the formula:
T = |r||F|sinθ
where r is the position vector, F is the force vector, and θ is the angle between the position vector and the force vector.
In this case, the position vector r = (4.0i - 2.0j) m and the force F = 20 N. The angle between the position vector and the force vector is 90 degrees, since they are perpendicular to each other.
Substituting these values into the formula, we have:
T = |(4.0i - 2.0j)| |20| sin 90° = (4.0)*(20) = 80 N·m.
Therefore, the torque of the force of 20 N about the origin is 80 N·m.