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Jul 2, 2021 at 15:59 comment added Jahan Claes @hbaromega The equality $\delta\vec d=\partial_k\vec{d} dk$ is really just a definition, but sure you can think of it as a Taylor expansion. As for your first question, it will probably help to draw a picture of the vectors $\vec d$, $\vec d +\delta \vec d$, and $delta\vec d$. In the limit $\delta\rightarrow 0$ we can find the angle in radians by taking the perpendicular distance between the two vectors and dividing by the length of the vector.
Jul 2, 2021 at 15:29 comment added hbaromega Sorry, could someone explain how the cross product between $\vec{d}$ and $\vec{\delta d}$ vectors represents the angle between $\vec{d}$ and $\vec{d}+\vec{\delta d}$? And $\vec{\delta d}=\partial_k \vec{d} dk$ can be checked by Taylor's series expansion?
Jun 22, 2020 at 21:16 comment added Karim Chahine Yeah I don't know how I've overlooked something so simple, thanks!
Jun 22, 2020 at 21:15 vote accept Karim Chahine
Jun 22, 2020 at 16:45 history answered Jahan Claes CC BY-SA 4.0