(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A force F=12NÎ-10NĴ acts on an object. How much work does this force do as the object moves from the origin to the point R=13mÎ+11mĴ?

2. Relevant equations

Work is the product of Force and Displacement (W=F*s)

3. The attempt at a solution

Things I know, or think I know: The object moves from the origin to a point 13 units to the right and 11 units up. The square root of the those two numbers squared and added together gives the magnitude which if up and right are both positive directions is a positive quantity of 17 if only two significant figures are considered. The force acting on this object has one component that is in the same direction, producing positive work, and one component that is in the opposite direction, producing negative work. The vector notation puzzles me. Do I split this into two different work situations for each component? I'm not sure where to start besides the conceptual thinking part. I can come up with the correct answer by figuring out W_{Î}=F_{Î}*s_{Î}and then subtracting W_{Ĵ}=F_{Ĵ}*s_{Ĵ}which gives the correct answer of 46 Joules but I'm not sure if this process will get me into trouble later on down the road. How would you do this problem? I want to know other methods. Thank you so much in advance.

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# Vector notation work problem

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