ABSTRACT
In the space surrounding us we can introduce the notion of an oriented volume as follows. Given three vectors a, b, c (in the original sense as equivalence classes of arrows), we call P(a, b, c):= {ra + sb + tc | 0 ≤ r, s,t ≤ 1} the parallelepiped spanned by a, b and c and denote by V(a, b, c) the volume of P(a, b, c). https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136547/a57ae1f0-6f59-46bd-bbdd-35a521b486a1/content/page159_1.tif"/>
