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Answer to Question #10407 in Mechanics | Relativity for harjyot singh

Question #10407
I just can't understand addition of vectors in components method, I have made diagrams and even read the theory but something keeps on nagging at the back of mind, see - I add two vectors aa^ and bb^ (not algebraically again) we get Rr ^ = aa^ + bb^ now breaking a and b = Rr^ = ai^ + aj^ + bi^ + bj^ rearranging it - Rr^= (ai^ + bi^) + ( aj^ + bj^) [ and now we can add those specifically as algebra cause they are in same direction) Rr^= (a+b)I^ + (a+b)j^ [Cannot add these algebraically ] Ie, Ri^ = (a + b)I^ and Rj^ = (a + b)j^ I even assumed it in the displacement way, but I guess I'm not comfortable with the '+' sign, at one point it just shows ' effect of vector s and vector t together ' and at one point we are actually(adding it ) and plus I'm not comfortable with 'break a vector into it's components and again the '+' sign muddles things here.. please help me clear this outright confusion.
Expert's answer
Dear visitor
Maybe you'll find this video helpful
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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