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$F_1 = -1.2 \times 10^2 \textrm{ N, } $$F_2 = 5.6 \times 10^2 \textrm{ N, } $$F_3 = -4.5 \times 10^2 \textrm{ N}$

Giancoli 7th Edition, Chapter 16, Problem 11

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when calculating the Force of 2, why isn't the force from 2 to 1 negative?

Hi moopen, thanks for the question. When calculating the net force on charge 2 we're interested only in forces exerted on charge 2. The charge 1 is exerting a force to the right on charge 2, so that force is taken as positive. It's true that charge 2 exerts a force to the left on charge 1 (this is the Newton's 3rd Law counterpart to the force exerted on charge 2 by charge 1), but this force isn't relevant since it isn't exerted on charge 2.

Hope that helps,
Mr. Dychko