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Existence of mutually perpendicular planes

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October 30, 2010
geometry unsolvedgeometry

Problem Statement

Let p,qp, q and rr be three lines in space such that there is no plane that is parallel to all three of them. Prove that there exist three planes α,β\alpha, \beta, and γ\gamma, containing p,qp, q, and rr respectively, that are perpendicular to each other (α⊥β,β⊥γ,γ⊥α).(\alpha\perp\beta, \beta\perp\gamma, \gamma\perp \alpha).
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