Look at it like this.
You have a box and you are applying 20 Newtons of force to the left, right, top, and bottom. Every force cancels each other out.
In trigonal planar, the forces are 120 degrees apart and their i and j vectors cancel each other out.
Just do the math.
(cos0 + cos120 + cos240) x 20N =
(sin0 +sin120+ cos240) x 20N=
I haven't calculated it, but both will give you 0.
That was the mathematical way of looking at it.