Oops... sorry, I didn't notice this till now. Just use kq/r^2 = 3.7E6 to calculate r. Draw a picture...The vector that cancels the first two charges I found to be <-1.3E6, 3.9E6>
The magnitude is 3.7E6.
How do I this is to find the distance the third charge is from A?
Are you sure your vector is right? I'm getting this for the field due to the first two charges:
For the first charge
this comes from (9E9)(85E-6)/(0.295^2)
For the second charge
this comes from (9E9)(85E-6)/(0.295^2 + 0.295^2)cos(45)
So the total I'm getting is:
<-3.1E6, 11.9E6> so with a magnitude of 12.3E6