Maximum of Three Mutually Perpendicular Lines in Ordinary Space

Theorem
In ordinary space, there can be no more than $3$ straight lines which are pairwise perpendicular.

Thus, in a configuration of $4$ straight lines in space, at least one pair will not be perpendicular to each other.

Proof
By assumption and popular belief, ordinary space (on the measurable local level) is an instance of a $3$-dimensional Euclidean space.

Hence the results of can be applied.

Let there be $4$ straight lines in space.

From Three Intersecting Lines Perpendicular to Another Line are in One Plane