Why don't you just change the basis vectors, make it simple, and check your own results? The work is just \$U_1-U_q=\frac{k}{r_1}-\frac{k}{r_q}\$ and \$U_2-U_q=\frac{k}{r_2}-\frac{k}{r_q}\$. Or am I missing something? I am just taking this off the top of my head, I admit. I may be forgetting something. But if not, this is an easy check to make without all the trouble maintaining both basis vectors shown in your work.
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