I'm reading a book on linear algebra, where the author gives a method to test the handedness or chirality of a given set of 3 basis vectors.
if (v1 x v2) . v3 > 0 then it's right-handed, while if it's less than 0, it's left handed.
While what beats me is that numbers are just numbers, left or right handedness of a system depends on the viewer and how he interprets the given data.
Taking the canonical i, j, k basis vectors, in both left and right handed systems i x j = k, thereby k.k = ||k||^2 > 0 (always), then how does this test hold true?