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I do not know how to approach this problem. Any hints will be helpful:

Let $u,\ v,\ w \;$ be three points in $\mathbb{R}^3$ not lying in any plane containing the origin.

Then which of the following are true?:

  1. $\alpha_1 u + \alpha_2 v + \alpha_3 w = 0 \implies \alpha_1 = \alpha_2 =\alpha_3 = 0$
  2. $u,\ v, \ w\;$ are mutually orthogonal
  3. one of $u, \ v, \ w\;$ has to be zero
  4. $u, \ v, \ w\;$ cannot be pairwise orthogonal
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    The question is maybe to choose which of 1,2,3,4 must be true, given that u,v,w not on a plane containing the origin. Is that it? In that case it looks like choice 1.2012-11-19
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    @coffeemath yes,you are right.2012-11-19
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    budha: I transcribed your question, from the image of it, directly into the post. Try, when possible, to type out your questions directly into the body of your questions; image links can "get lost" over time, and for reasons related to accessibility (for the blind, e.g.), it's best to type out questions (and formating in LaTeX is always good, too!).2012-11-19

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