so, if i want to treat E as a vector, i must relate it to a certain point? i thought the field was a vector anyhow, so i can add it however i wanted.
i'm adding a picture that might make things clear. the green arrows are E exerted by a single charge at (0,0,0). so, from symmetry, you argue that E in that axis cancels each other, but can't you say as well, that if you were to add them up (0,y,0)+(0,-y,0) you'd get the same answer? -note that i refer to E outside the box, as i understand that inside (from gauss law) the field is zero in any case
edit: i think i'm getting it: i can treat E in that manner if, like you say, i have a point on which E is exerted, but if i'm talking about a sphere / cube / other as a shape, there is no point for which i can add the vectors?
thank for your patience, when i get things slow, i understand them fast :)