Can orthogonal vectors have some values that are the same? such as are (1,2,5) and (1,2,-5). orthogonal as the dot product is zero?
Thanks in advance!
Just think of the orthogonal standard basis $(1,0,0), (0,1,0)$ and $(0,0,1)$. If you take them two by two, they always have a zero in common. When asking yourself questions about "does an example satisfying blablabla property exist?" try to think of the examples you know that are the easiest first ; then if they don't work you start thinking about weird examples.
Hope that helps,