Show that if there exists any two vectors (v and u) in R^3, and their length is equal such that : ll u ll = ll v ll then u+v will be orthogonal to u-v
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nonzero vectors are orthogonal if their scalar product is 0.
(u+v).(u-v)
= u.u - u.v + v.u - v.v
= (||u||)^2 - (||v||)^2 since u.v = v.u
= 0 since ||u|| = ||v||
(u+v).(u-v)
= u.u - u.v + v.u - v.v
= (||u||)^2 - (||v||)^2 since u.v = v.u
= 0 since ||u|| = ||v||