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** Q 2538291102. ** 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 three points other than origin, then prove that the pernmtation [A', B', C'] of [A, B, C] exists. Such that

(a) A lies on `L_1 , B` lies on `P_1` not on `L_1`, C does not lie on `P_1`

(b) A' lies on `L_2 , B'` lies on `P_2` not on `L_2`, C' does not lie on

**JEE 2004 Mains **