When I went to college the dot was used for the dot product (scalar product) of two vectors while the cross was used for the cross product (vector product) of two vectors.
Since in this case numbers (read: one-dimensional vectors) are multiplied, the dot product is used, which should be denoted by a dot.
(But really, if I were to write a formula in Latex I would just use the * symbol, too.)
But I almost always poop at work :(