General solutions of two quadratic functional equations of Pexider type on orthogonal vectors

Basing on the studies on the Hyers-Ulam stability and the orthogonal stability of some Pexider-quadratic functional equations, in this note we find the general solutions of two quadratic functional equations of Pexider type. Both equations are studied in restricted domains: the first equation is studied on the restricted domain of the orthogonal vectors in the sense of Rätz, also the second equation is considered on the orthogonal vectors in the inner product spaces with the usual orthogonality.