If 2 vectors, v and w in 3D have the same length, then v-w and v+w will always be orthogonal...is this true?

If vectors are orthogonal then their dot product will be 0.


(v - w).(v + w) = v.v - w.w = |v|*2 - |w|^2 = 0 since w and v have the same magnitude (I used |v| as the magnitude of v and so on)





So yes what you say is true (unless of course v = w)

Cats