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Answer 1 · 2017-11-10T13:37:17

See below.

If #norm(u+v)=norm(u-v)# then

#norm(u+v)^2= norm(u-v)^2# or

#normu^2+2 << u,v >> + norm v^2 = norm u^2 - 2 << u,v >> + norm v^2#

or

#<< u, v >> = 0# then assuming that #norm u > 0, norm v > 0#

we conclude that

#u, v# are orthogonal.