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

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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?
 
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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.
 
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What dimension is the vector [0,0,0] in? For example, I know that vector [o] is in dimension zero
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.
, but would [0,0,0] be in that too? Or, is it classified as being in R3 since there are three components?
 

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