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What dimension is the vector {0,0,0} in?

  1. Nov 1, 2012 #1
    What dimension is the vector [0,0,0] in? For example, I know that vector [o] is in dimension zero, but would [0,0,0] be in that too? Or, is it classified as being in R3 since there are three components?
     
    Last edited by a moderator: Nov 2, 2012
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  3. Nov 1, 2012 #2

    LCKurtz

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    It is the zero vector in ##R^3##. ##R^3## is a 3-dimensional vector space and that zero vector is one of its elements.
     
  4. Nov 2, 2012 #3

    Mark44

    Staff: Mentor

    No, this is a vector in R, which can be considered a vector space of dimension 1. Every vector in this space, including the zero vector, has a dimension of 1.
     
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