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Positive work is input energy, w= -f.d - |fd|cos(fd) , when this is positive energy is put into the system, in this case the force is in the opposite direction of the displacement. Negative work is output energy properly called exergy, w = -f.d, in this case the force is in the direction of the displacement, for example, dropping a ball is exergy, the displacement is in the direction of the force of gravity. This is exergy, work is taken out of the system as opposed to lifting the ball which required putting work into the system.

Maxwell had a problem with quaternions because physicists defined positive work as dropping the ball, and the rules of quaternions said dropping the ball is a negative sign and thus exergy, work out, not work in. Around the 1900 this was a major conflict and the physicist won and decided to change the sign on vectors squared , I2 = -1 to +1, so dropping the ball would be positive energy.

This is incorrect physics and incorrect mathematics. The sign of the scalar work is negative for work out and positive for work in. This is seen in opposites attract, you get work out and the sign is negative. For like charges the sign is positive and you have to put work in.

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Q: What do you mean by positive and negative work?
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