Module 2: The Cross Product
A second useful product computation is the cross product. But this operation is restricted only to vectors in R3 (whereas the dot product is defined for vectors in any (natural) dimension.)
Let →a=(axayaz) and →b=(bxbybz)
Then we can define:
→a×→b=(aybz−azbyazbx−axbzaxby−aybx).
This is a very awkward definition, but can be made nicer if we think about the pattern illustrated in the following picture:
For those of you who have computed the determinant of a three by three matrix, this pattern should be familiar.
Example:
(−112)×(03−2)=(−2−60−2−3+0)=(−8−2−3)