Question about orthogonality
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Question about orthogonality

[From: ] [author: ] [Date: 11-12-20] [Hit: ]
(u-v)= u.u - u.v + v.u - v.v= (||u||)^2 - (||v||)^2 since u.v = v.......
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||
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