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When they say "breake vector into its components" it means that you establish system of coordinates(commonly Oxy) and write your vector as a sum with some coefficients of basic vectors i,j of this system. As your vectors a,b, are each the sum of vectors i,j(basic){i.e. you break them into components} you as well find their sum a+b as a sum of those basic vectors(i.e. you simply add numbers beside same vectors, collecting together components with i and with j)
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