Given two vectors #vec a, vec b# their sum is
#vec s = vec a + vec b#. Now computing the norm of #vec s# and squaring
#norm (vec s)^2 = norm( vec a + vec b)^2 = norm (vec a)^2+2 << vec a, vec b >> + norm( vec b)^2#
The scalar product
#<< vec a, vec b >> = norm vec a norm vec b cos(hat(vec a, vec b))# has a maximum when #cos(hat(vec a, vec b))=1# and a minimum when #cos(hat(vec a, vec b))=-1# so
#min norm(vec s)^2 = norm (vec a)^2+norm(vec b)^2-2norm vec a norm vec b# and
#max norm(vec s)^2 = norm (vec a)^2+norm(vec b)^2+2norm vec a norm vec b#
Finally, when two vectors #vec a, vec b# are aligned, their sum is a minimum or a maximum deppending on their relative orientation:
concordant a maximum
discordant a minimum
