I need to understand orthogonality. I am monitoring QM lectures by Dr. Physics A, and he said all basis states of a state are orthogonal. I can understand that for the topics like polarization or spin, where Cartesian coordinates obtain with reference to measurements in one of 3 perpendicular-to-each-other axes, but then he gets into the linear position operator. Every point on the line is a basis state, and their number is infinite. I understand that if a particle is at one point it is definitely not at another, so that seems to fullfill a criterion for orthogonallity, but how can they be orthogonal (perpendicular) to each other? I cannot picture it.