Vectors in Dimensional Analysis

Huntley suggested to increase the number of independent dimensions by employing vector characteristics for some of the parameters. His technique lead to a number of inconsistencies. In some problems, the results are completely in error, e.g., by canceling the dimensional representation of a vector product against the representation of a scalar product of the same two vectors. The difficulty is resolved by introducing the dimensional representation of the unit vectors which enter as additional primary dimensions. The examples illustrated that this may lead to dependence between the primary dimensions. Yet, in many problems, it leads to an increase in the number of independent dimensions as well. This results in a reduction of the resulting dimensionless II-terms.