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.Jacob959 said:What dimension is the vector [0,0,0] in? For example, I know that vector [o] is in dimension zero
Jacob959 said:, but would [0,0,0] be in that too? Or, is it classified as being in R3 since there are three components?
The vector {0,0,0} is in the zeroth dimension. This is because it has no magnitude in any direction and can be thought of as a single point in space.
Yes, {0,0,0} is considered a vector. While it may not have any magnitude or direction, it still follows the definition of a vector which is a quantity with both magnitude and direction.
Yes, a vector can exist in multiple dimensions. For example, the vector {2,3} can exist in both two-dimensional space and three-dimensional space.
The dimension of a vector is important because it tells us the number of components or directions in which the vector can vary. It also helps us understand the properties and behavior of the vector in different spaces.
Yes, {0,0,0} is the only vector in the zeroth dimension. This is because any other vector with non-zero components would have magnitude and direction, thus placing it in a higher dimension.