solution:

First find the distance from charge a to charge b:

eqnarray12

Now find the force exerted by charge b on charge a:

eqnarray18

The negative sign in the answer means that there is an attraction (unlike charges) so the direction is straight down, towards charge b.
Now for the force exerted by charge c on charge a:

eqnarray32

The positive sign in the answer means that there is a repulsion (like charges) which means that the direction is away from charge c so 30 degrees above horizontal to the left.

Now the resultant vector of these two vectors must be found. I will use the law of cosines, but you could also break up the vecors into their x and y components and just add them up:

eqnarray46

Now we have the magnitude, we just need to find the angle. I use the law of sines:

eqnarray58

The force is tex2html_wrap_inline84 exerted at tex2html_wrap_inline86 west of south.

Note: This problem also shows the nature of the coulomb. One coulomb is a huge charge. Usually you deal in microcoulombs, for as you can see, putting such charges at this distance would cause a HUGE force.