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Two positive charges q1 and q2 are located at the points with radius vectors r1 and r2. Find a negative charge q3 and a radius vector r3 of the point at which it has to be placed for the force acting on each of the three charges to be equal to zero.

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Let us choose coordinate axes as shown in the figure and fix three charges, q1 , q2 and q3 having position vectors  respectively.

Now, for the equilibrium of q3.

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