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

[hasibx]

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?

 

[haruspex]

We would need to know the positions of the masses in terms of the coordinate system.

 

[hasibx]

We would need to know the positions of the masses in terms of the coordinate system.

 

[haruspex]

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.

 

[phinds]

@hasibx you do not seem to understand what it means to

know the positions of the masses in terms of the coordinate system.

WHERE do the points sit relative to the x-y coordinates?