Question

The point charges in the figure below have the following values: q₁ = +2.7

Answer 1

the magnitude of the force on each of two point charges
(when there are only two) is k Q1 Q2 / r^2, where k = 9*10^9

If the magnitude of the force exerted on q2 in this problem is 0.63 N,
and if I put q1 at the origin of the coordinate system, then
(k q1 q2 / d^2) (i/2 + j sqrt(3)/2) + (k q2 q3/d^2) (-i/2 + j sqrt(3)/2)
= some force vector whose magnitude turns out to be 0.63 N. So,
(k q2 / 2 d^2) [ (q1-q3) i + (q1+q3) j sqrt(3) ] has a magnitude of 0.63 N.
d^2 = ( k q2 / 1.26 N ) | 3.58 uC i + 1.81 sqrt(3) uC j |
= (k q2 / 1.26 N) [ 4.75* 10^(-6) C ]
= 9*10^9* 6.3*10^-6* 4.75*10^-6 m^2
=    0.269325
d = sqrt(0.269325) meters = 0.518965 m = 0.52 m

The direction of the net force is easier, we don't
care about k or d or the magnitude of q2 (though its sign matters).
The direction of (q1-q3)i + (q1+q3)j is
the direction is arctan ((1.81 sqrt(3))/3.58) = 0.719 rad = 41.19 degrees
(measured counterclockwise from the axis q1 q3).