I'm reviewing my old calculus textbook and I stumbled upon a proof of Kepler's First Law of Planetary Motion which uses vector valued functions along with all of the operations to demonstrate the material. I understand the math and how to to DO it but what I am struggling with is why.(adsbygoogle = window.adsbygoogle || []).push({});

It goes from:

vXh= GMu+c

and then does the dot product of both sides withr.

Why is the above equation "dotted" withr.

This is apparently found in most calculus textbooks but if it is not:

vis the velocity

uis the unit vector of direction

his a constant vector ofrXv

cis a constant vector of integratingu'

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# Kepler's First Law of Planetary Motion

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