Orthogonality v. Perpendicularity

Question

In Intro to Linear Algebra (my class) two vectors are defined to be orthogonal if their dot product is zero. And the dot product of two $n$-vectors $\vec a\cdot\vec b=0$ means that the two vectors are perpendicular provided that $\vec a\neq\vec0,\vec b\neq \vec0$. But what if the dot product is between a non-zero vector and the zero vector, are the non-zero vector and zero vector still considered considered orthogonal even though they are not perpendicular? Wikipedia defines orthogonality to be perpendicular.

Answer 1

Wikipedia also says that orthogonality is generalizing that idea into $n$ dimensions. I only hear people say perpendicular when they are talking about 2-3 dimensions. In which case they are the same thing.

I think the zero vector is usually considered orthogonal to every other vector. You could say that the zero vector is perpendicular to every other vector, but I think when people use that term they view the zero vector as a case that doesn't come up (e.g. lines of non zero length), so typical try to omit the situation in the definition.