Gravitational Forces on three masses at the corners of an equilateral triangle

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The discussion focuses on the gravitational forces acting on three masses positioned at the corners of an equilateral triangle. The mathematical solution presented involves the vector rule, resulting in a force expression that includes a negative component, specifically (-\hat{j}). The question raised concerns the necessity of knowing the coordinate positions of the masses to understand why the negative sign is used. It is emphasized that without a clear definition of the coordinate system, the assumption of the direction of (-\hat{j}) may lead to confusion. Clarifying the positions of the masses in relation to the x-y coordinates is essential for accurate interpretation of the results.
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Homework Statement
Three identical masses m are kept at the vertices of equilateral triangle of side 'a'. Find the force on A due to B and C
Relevant Equations
F =\frac{Gm_{1}m_{2}}{r^2}
I solved the math using vector rule
R= \sqrt{F^2 +F^2 +2F^2cos\frac{\pi}{3}} =\sqrt{3}\frac{Gm^2}{a^2}
But the answer is showing: \sqrt{3}\frac{Gm^2}{a^2} (-\hat{j})

My question is:

Why is (-\hat{j}) added here? Why is it negative?
 
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We would need to know the positions of the masses in terms of the coordinate system.
 
haruspex said:
We would need to know the positions of the masses in terms of the coordinate system.
 

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That's not what I asked for, but the given answer seems to be assuming that ##\hat j## is straight up the page in that diagram. If you were not told that then I do not see how you could be expected to get that answer.
 
@hasibx you do not seem to understand what it means to
haruspex said:
know the positions of the masses in terms of the coordinate system.
WHERE do the points sit relative to the x-y coordinates?
 
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