Coulomb force and charge equilibrium on the xy-plane

[PRASHANT KUMAR]

Homework Statement

Two point charges q and 4q are located at r1 and r2, respectively, on the xy- plane. The magnitude Q and location R of a third charge to be places on the plane such that the total force on each of the three charges vanishes, are?

first i plotted the problem on the xy coordinate system and then the position vectors of two charges q and 4q as r1 and r2 and then i kept the charge Q at R and then i calculated the sum of forces on the charge q by the two other charges and equated to zero. And again using coulomb force relation i equated the sum of forces on charge Q by q and 4q then i calculated the values of Q and R

i am getting R=(2r1+r2)/3 and Q= 4q/9 but the options are

1. Q= -4q/9 and R= (2r1+r2)/3
2. Q= -4q/5 and R= (r1+2r2)/3
3. Q= -4q/25 and R= (16r1+r2)/17^(1/2)

4.Q= -9q/4 and R =(r1 + 2r2)/3

in calculating the above problem i was equating the magnitude of the forces .
So, is my answer correct or not?
if not then how to calculate that ?

 

[haruspex]

am getting R=(2r1+r2)/3 and Q= 4q/9

It clearly cannot have the same sign as q. That would subject q and 4q to net forces pushing them away from Q. Please post your working.