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

Question

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.

Answer 1

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)