A companion article introduced a set of orthonormal opponent color matching functions (CMFs). That orthonormal basis is an expedient for plotting lights in Cohen's logical color space. Indeed, graphing the new CMFs together (as a parametric plot) gives Cohen's invariant locus of unit monochromats (LUM). In this article, the functions and related vector methods are applied to fundamental problems. In signal transmission and propagation-of-errors work, it is desirable to describe stimuli by decorrelated components. The orthonormal CMFs inherently do this, and an example is worked out using a large set of color chips. Starting with the orthonormal functions, related functions, such as cone sensitivities, are graphed as directions in color space, showing their intrinsic relationships. Building on work of Tominaga et al., vectorial plots are related to the problem of guessing the illuminant, a step toward a constancy method. The issue of color rendering is clarified when the vectorial compositions of test and reference lights are graphed. A single graph shows the constraint that the total vectors are the same, but also shows the differences in colorimetric terms. Since the LUM summarizes a trichromatic system by a three-dimensional graph, dichromatic observers can be represented by 2-D graphs, revealing details in a consistent way. The fit first method compares camera with human, applying the Maxwell-Ives criterion in graphical detail. (c) 2011 Wiley Periodicals, Inc. Col Res Appl, 2011.