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engineering810

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I am in engineering 2 at my school and have been trying to figure out why a homework problem has the answer it has. The question and answer is posted below. My question is, how should I have known the angle between the two vectors (when using parallelogram law) should be a 90 degree angle? I understand the length of a vector corresponds to it's magnitude so why shouldn't the angle from Fa to the vector connecting Fa to Fr be 60 degrees since that would've caused the shortest distance to the resultant force? I do not want to continue studying until I understand this so any help would be greatly appreciated. Thanks in advance!

(Problem and answer)

http://www.flickr.com/photos/102827963@N02/9992475615/

http://www.flickr.com/photos/102827963@N02/9992475665/