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Two planes P1 and P2 pass through origin...

Two planes `P_1` and `P_2` pass through origin. Two lines `L_1` and `L_2` also passing through origin are such that `L_1` lies on `P_1` but not on `P_2`,`L_2` lies on `P_2` but not on `P_1`. A,B, C are there points other than origin, then prove that the permutation [A', B', C'] of [A, B, C] exists. Such that: A lies on `L_1`, B lies on `P_1` not on `L_1`, C does not lie on `P_1` .

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