I got these 3 questions for my homework. I tried it nearly a whole day but...
**A cube of edge a carries a point charge q at each corner. Show that the resultant electric force on any one of the charges is given by
F = 0.262(q^2)/ε(a^2)

Here is my picture of the problem and my work
http://img4.imageshack.us/img4/441/003bgk.jpg
The only thing I'm in trouble with is how can I find F act on 1 'cause of 6 (F16) ? The book gives me something with radical 3 along with i, j, k; but I just don't get how they are there.
**Where can you place a second point charge q (equal to the charge on the rod) so that q' is in equilibrium (ignore gravity)? Solve this problem assuming that (a) q is positive and (b) q is negative.

I tried to get a picture of the problem and some of the forces drawn
http://img691.imageshack.us/img691/5360/002akh.jpg
Since q' has to be in equilibrium, that means sum of the forces must be 0, so I thought that: dF + dFy + (something) = 0. But the problem is I don't know what is that "something" is. Is it gonna be another dF' of the second charge (q), or what? I'm kind of lost.
** Last question, the book gives me an example of Ring of Charge with q' on the z axis. But my question is what if q' is not on z axis? Like maybe a little bit next to the right of the z axis instead? Is there going to be any change in my calculations?

Here is the picture of the book example and my summarized work
http://img231.imageshack.us/img231/7632/001sqj.jpg
Please help me
. I'll really appreciate.