This is a pedantic question about the use of the terms 'orthogonal' and 'perpendicular.' I think when people first hear the term 'orthogonal' they learn it to mean perpendicular, but in the linear algebraic sense, I believe it simply means that the inner product between two vectors is zero. This has no geometrical extension: just take a function space, for example.
But even if we are working in, say, $\mathbb{R}^2$, I could define an inner product that is not the standard one, such that two vectors that are $\it{orthogonal}$ are not $\it{perpendicular}$. So in this sense, perpendicularity is a purely geometrical adjective, referring to $\bf physical$ $90^{\circ}$ angles. Is this interpretation correct?