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?:
- $\alpha_1 u + \alpha_2 v + \alpha_3 w = 0 \implies \alpha_1 = \alpha_2 =\alpha_3 = 0$
- $u,\ v, \ w\;$ are mutually orthogonal
- one of $u, \ v, \ w\;$ has to be zero
- $u, \ v, \ w\;$ cannot be pairwise orthogonal