Scalar product of position vectors

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SUMMARY

The discussion focuses on finding the minimum and maximum distances between position vectors using the scalar product. The key insight is that the vector r represents the difference in position, while the expression r . r denotes the square of its length, which is essential for calculating distances. To determine extrema of a function f(t), one must differentiate and solve for f'(t) = 0. This approach simplifies the problem by allowing the minimization or maximization of the square of the distance instead of the distance itself.

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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 don't understand the significance of r.r, however.

Thanks
 
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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