Conceptual question about Newton second law

[edgarpokemon]

Homework Statement

There are two forces on the 2.08 kg box. F1 is 20.5N. acceleration is happening in the third quadrant with a magnitude of 12.1m/s^2 and with an angle of 25.9 (in the third quadrant). Find the second force in vector notation.

Homework Equations

Fnet=ma

The Attempt at a Solution

My question is this. In the picture, the acceleration is occurring at the third quadrant. So I assume that the second force will have negative x and y components, because acceleration has also negative x and y components in that quadrant. So for the x-component of the acceleration, I used F1-F2=m(-acos(25.9)) so F2=m(acos(25.9)+F1. I am assuming acceleration is negative because it is pointing down. in the solution, it tells me that I should use instead F1+F2=ma. But why is there a + sign in F2? since F2 will point in the opposite direction of F1, shouldn't there be a negative sign for F2 instead?

 

[J Hann]

Shouldn't the sum of Fx1 and Fx2 = m ax, for example, where F1 and F2 are vectors?
The scalar components of these vectors may have negative signs.