There are three such vectors in the Euclidean space $E^3$ that all their pairwise inner products are non-negative. Does there always exist such orthonormal basis in $R^3$ that all these three vectors lie in one coordinate octant?
From the first part, I understand that these three vectors will be having the same signs respectively such that their pairwise inner dot product is non-negative. But the second of the question is quite confusing. I do not understand what is the question trying to ask. Is it asking to find an orthonormal basis that is orthogonal to all the three vectors such that they all lie in one octant? But since the vectors are arbitrary it is not easy to find the orthonormal vector. How should I proceed?
Any help is appreciated. Thanks in advance