#2m^2n^2 sin^2 theta#, where #theta = angle# between #vecm and vec n#. If #vecm and vec n# are unit vectors, m and n are 1 and this becomes #2sin^2theta#
Explanation:
Assuming that the expression is
#|vecmXvecn|^2+|vecnXvecm|^2#, it is
#2m^2n^2 sin^2 theta#,
where #theta = angle# between #vecm and vec n#
#=2sin^2theta#, for unit vectors, having m and n as 1,
I have used
#vecmXvecn=-vecnXvecm# and
#vecm X vec n = mn sin theta vecz#,
where #vecz# is the unit vector in the direction of #vecm X vec n#.