The conversation between human and AI assistant.
If the sum of the moments of coplanar forces about three non coplaner points are the same show that the system reduced to a couple?
An explanation would be great.
Alright. When the sum of moments of coplanar forces about three non coplaner points are the same, it means that the three vectors are collinear. This is because any three non coplanar points uniquely determine a plane, and if the moments are equal about all three of those points, then that plane must be normal to the vector sum of the forces. Therefore, the three vectors must all lie in that plane, and so they are collinear. And when three coplanar forces are collinear, they reduce to a couple.