Let $d_1, d_2$ and $d_3$ be three non coplanar concurrent lines and $O=d_1\cap d_2\cap d_3$. In each line we place three points (2 by 2 distinct) $A_i,B_i$ and $C_i$, $i\in \{1,2,3\}$such that $A_i\in d_1$, $B_i\in d_2$ and $C_i\in d_3$. We suppose that $\frac{2}{\overline{OA_2}}=\frac{1}{\overline{OA_1}}+\frac{1}{\overline{OA_3}}$ and two analogous relations.

  1. Find all planes $A_iB_jC_k$ so that $i+j+k=6$

  2. Find equations of each plane by using an adequate coordinates systems.

  3. We suppose that three of the planes found at 1. have a common point, show that all planes are concurrent.

For the first question I’ve found planes $A_1B_2C_3$ $A_1B_3C_2$... seven planes at all.

  • $\begingroup$ None has a solution or a hint. $\endgroup$ – HAMIDINE SOUMARE Mar 4 at 23:45

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