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

[Jacob959]

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?

 

[LCKurtz]

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.

 

[Mark44]

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?