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I have here one important abstract question which makes up some perplexity to my understanding. Attached to this post is one pic of F and two new introduced axes ( u and v ) . Let us for instance not consider them as perpendicular to each other. Now, if I am asked to resolve these forces along u and v USING geometry, I will use the parallelogram rule which will outcome results rather than F cos theta as for the u axis for example. Now, if we want to compute the scalar projection of F along u, we simply can say it is F. unit vector f u which will be F cos theta. However, written in some books, this magnitude is NOT the same as the component of F along u. Why?? To sum up my question, what is the difference between the component of F along any axis using the parallelogram rule and the dot product definition. Sorry for elongating and Thanks to whoever gives me a kind hand.

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# Difference between Force components using triangle rule and dotproduct

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