The sign permutation in the rotation matrix and the formulation of the collinearity and coplanarity equations

Abstract

Two basic variations arise in the formulation of the collinearity and coplanarity equations. These two variations are generally referred to as the diapositive equation and the negative equation. The relationship between these two formulations and the rotation matrices is investigated in this study. This study has revealed that the sign changes of principal distance in both the collinearity and coplanarity equations are coupled with the sign permutation of the elements in a rotation matrix.