21. The vector, and so the cross product, comes from the product of this bivector with a trivector. 22. The components of the bivector are the projected areas of the parallelogram on each of the three coordinate planes. 23. These bivectors are summed to produce a single, generally non-simple, bivector for the whole rotation. 24. Note that the order is important because between a bivector and a vector the dot product is anti-symmetric. 25. If the electric and magnetic fields in ! 3 are and then the " electromagnetic bivector " is 26. As a whole it is the electromagnetic tensor expressed more compactly as a bivector , and is used as follows. 27. The bivector magnitude ( denoted by ) is the " signed area ", which is also the determinant. 28. Two bivectors, two of the non-parallel sides of a prism, being added to give a third bivector . 29. It's not fundamentally a vector ( oriented line element ), but an oriented area element ( bivector ). 30. Where is the bivector form of the electromagnetic tensor, is the four-current and is a suitable differential operator.