# Coordinate system handedness

1MileCrash
How do you define a right handed coordinate system for a basis which is not orthonormal?

voko
When you use the right hand rule and actually try to do that with your hand, you almost always get a non-orthonormal basis. If the angles between you fingers are very oblique, that is a good example; non of the angles may be zero, however.

More formally, it should be any three vectors not pairwise collinear, and forming a right-hand triad.

1MileCrash
Book just says scalar triple product positive for right hand, negative for left...

voko
Yeah, it boils down to that. One caveat is that it depends on the definition of the vector product, which itself includes right-handedness.

1MileCrash
That's interesting.. so really, if it is negative it means it "differs" from the way we have defined the vector product (right handed.)

Thanks.