- #26

- 27,567

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Doesn't #1 imply #2? #1 says that the change in the vector must be orthogonal to the vector. (More precisely, the argument that establishes #1 establishes this--at least I think it does*.) Any such change can only change the direction of the vector, not its magnitude.I don't think either statement implies the other in general.

I agree that #2 does not imply #1 for a null vector, so the two statements are not equivalent.

* - The argument that establishes #1 is that ##R_{aacd} = 0##. If we use orthogonal coordinates, this statement is the same as saying that the change in the vector must be orthogonal to the vector. If we use non-orthogonal coordinates, that is not necessarily the case; however, since we can always find orthogonal coordinates, I think the argument still establishes that the change in the vector must be orthogonal to the vector.