Q: Is there a name for this operation (involving a dot product)? I want to describe this operation in a paper. Its a formula for the size of a dimension in a hypothetical manifold. The dimensions are {R,B,M} (Red, Blue, Magenta):
$$y^M=\tau^R \boldsymbol{\vec{e_R}}\cdot\tau^B \boldsymbol{\vec{e_B}} + y_1^R\tau^R + y_1^B\tau^B$$This formula states that $y^M$, the size (extent) of the magenta (M) dimension (in units of $\tau^2$),is the dot product of $\tau$ coordinates plus a proportion of the $\tau$ coordinates. $y_1^R$ and $y_1^B$ are constants of proportionality with units of $\tau$.
If there's no existing name for this operation, then how would you describe it? The best I've developed is

The extent of the magenta dimension, $y^M$, is the sum of the dot product and a proportion of the $\tau$ coordinates.

