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Insights Frequently Made Errors in Vectors - Elementary Use - Comments

  1. Mar 3, 2016 #1


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  2. jcsd
  3. Mar 4, 2016 #2


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    Generally good insight as usual, but I feel I must nitpick a bit here, since you are mentioning the issue of vectors belonging to a position:
    While this may be true for the most basic use of vectors in terms of vectors in a Euclidean space, it is not generally true. For the more general vector concept, every vector is associated with a position and belongs to the tangent (or cotangent) space at that position.

    Position is generally not a vector. Velocity belongs to the tangent space at the position of the object, as does acceleration. In a Euclidean space the position of the velocity vector may often be ignored as parallel transport is trivial, but consider movement on a sphere (such as the Earth's surface) for example.
  4. Mar 7, 2016 #3
    What an incredible resource this series has become!
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