Learning moments in statics currently

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The discussion focuses on resolving a force into its x and y components and applying Varignon's Theorem to find moments at different points on a diagram. The user expresses confusion over the distinction between the "vector approach" and the principle of moments, questioning whether they are essentially the same. It is noted that the vector approach involves using both a force vector and a distance vector. The user seeks clarification on how to proceed with the problem given the unclear definitions in their text. Understanding the differences between these concepts is crucial for solving the problem effectively.
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We are learning moments in statics currently, and I have a problem that asks me to resolve the force given into x and y components, then, using "the principle of moments" aka Varignon's Theorem, find the moment with that same force applied at different points on the diagram, all of course resulting in the same moment about the given point.

That is easy enough, however, the last part of the question asks me to find the moment using "a vector approach". It seems to me, based on both my opinion and the rather unclear description of vector approach given in my text, that the principle of moments and vector approach are the same thing...Based on that, am I am unsure how to proceed..

What is the difference between "vector approach" and "the principle of moments", aka Varignon's thm.?
 
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Using vectors requires two vectors, both a force and a distance vector.
 

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