Question

What r dimensions and units of unit vectors?

Answer 1

They can have coordinates relative to a basis, that basis usually being the standard basis.

1.A vector space has a dimension, that dimension being the number of coordinates for any vector in it. For example, R2R2 has two dimensions, and a vector in it, like (35,45)(35,45) has two coordinates.

2.That example vector is also a unit vector.

Unit vectors, like all vectors, have the same number of coordinates as the dimension of the space to which they belong.

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Answer 2

the dimension of unit vector depend on the quantity.
Each unit vector has magnitude =1
and a specific direction.
The dimension of unit vector is same as the particular vector quantity,and so is the unit