More Gauss practice (hard)

Two identical point charges \(+q\) are placed on the x-axis at \(\pm 5~\mbox{cm}\). As we know, the total electric field produced by the charges is often visualized using field lines. Consider two particular field lines, one from the left charge (Line A) and one from the right (Line B). The tangent vector to Line A is (1,1) when it leaves the left charge and the tangent vector to Line B is (-1,1) when it leaves the right charge. What is the minimum distance \(d_{min}\) in centimeters between these two lines?

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