Maxima vector magnitude and cross product

As far as I know, there is no built-in function to calculate a vector's magnitude, but you can easily define your own:

(%i1) norm(x) := sqrt(x . x)$
(%i2) norm([1, 1]);
(%o2)                               sqrt(2)

The cross product operator ~ is only available after loading 'vect':

(%i1) load("vect")$
(%i2) [1, 2, 3] ~ [2, 3, 4];
(%o2)                        [1, 2, 3] ~ [2, 3, 4]
(%i3) express(%);
(%o3)                            [- 1, 2, - 1]