in mathematics the cross products are the binary operation on two vectors in a 3dimensional Euclidean space that results in another vector which is perpendicular to the containing the 2 inputs vector.

In Euclidean geometry, yes.

In Euclidean geometry, yes.

In Euclidean geometry, yes.

In Euclidean geometry, yes.

nothing

In a Euclidean space, the shortest distance between two points is a straight line, so no.

One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.