It was then shown how the determinant of a 3 by 3 matrix can be defined in terms of the anti-symmetric tensor, and how this corresponds to the usual definition of a determinant.
Tensor notation was then used to prove the two most difficult vector identities, number 5 and number 6. The latter required a useful identity which expresses the product of two anti-symmetric tensors summed over a common index in terms of Kronecker deltas.
Armed with these two vector identities, we then went back to calculate the magnitude of the cross product of two vectors. It turns out to be the product of the magnitudes of the original two vectors times the sine of the angle between them!
Some problems were given, which will be part of assignment #02, due next Friday, September 24th.