IB Physics Point Charges at the Corners of a Triangle

This tutorial sheet investigates a problem involving two positive and a negative charge placed in a plane. It is taken from Electricity and Magnetism, The Berkeley Physics Course Volume 2, Second Edition by Edward M Purcell.

1. Two positive ions and one negative ion are placed at the vertices of an equilateral triangle. Where can a fourth charge be placed so that the force on it will be zero? Is there more than one such place? (page 35 q 1.12)