Areal velocity equal to the magnitude of the cross product of vectors "AB" and "AC". This area can also be viewed as a vector with this magnitude, pointing in a direction perpendicular to the parallelogram; this vector is the cross product itself: Hence The areal velocity is this vector area divided by Δ"t" in the limit that Δ"t" becomes vanishingly small: But, formula_4 is the velocity vector formula_5 of the moving particle, so that On the other hand, the angular momentum of the particle is and hence the angular momentum equals 2"m" times the areal velocity. Conservation of areal velocity is a
Product of group subsets "ST", then "ST" coincides with the semidirect product of "S" and "T". Finally, if both "S" and "T" are normal in "ST", then "ST" coincides with the direct product of "S" and "T". If "S" and "T" are subgroups whose intersection is the trivial subgroup (identity element) and additionally "ST" = "G", then "S" is called a complement of "T" and vice versa. By a (locally unambiguous) abuse of terminology, two subgroups that intersect only on the (otherwise obligatory) identity are sometimes called disjoint. A question that arises in the case of a non-trivial intersection between a normal subgroup "N"