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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!

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These two are not orthogonal :) –  Artem May 12 '12 at 19:17
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$(1,2,5) \cdot (1,2,-5) = 1 + 4 -25 = -20 \ne 0$, so they arent orthogonal, but $(1,2, \sqrt 5)$ and $(1,2,-\sqrt 5)$ are, so the answer to your first question is yes. –  martini May 12 '12 at 19:17
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1 Answer

up vote 2 down vote accepted

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,

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