Scalar product of position vectors

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Suppose, in general, that you have a function f(t). How do you find its minimum and maximum (i.e. the extrema)?

[Hint: it involves differentiation]
find values of t for f'(t) =0

I dont understand the significance of r.r, however.



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Well, r is the vector that describes the difference in position.
r . r is the square of its length. So the square of the distance between the particles.

Note that minimizing (maximizing) the distance is equivalent to minimizing (maximizing) the square of the distance.

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