P_(1) and P_(2) are planes passing through origin, L_(1) and L_(2) are two lines on P_(1) and P_(2) respectivelym such that their intersection is the origin. Show that there exist points, A, B and C , whose perpmutation, A, B' and C' respectively, can be chosen such that (i) A is on L_(1) 'B and P_(1) " put not on " L_(1) and C not on P_(1) , (ii) A is on L_(2) , B' on P_(2) " but not on " L_(2) and C' " not on" P_(2) .

P_(1) and P_(2) are planes passing through origin, L_(1) and L_(2) are

1.	P_(1) and P_(2) are planes passing through origin, L_(1) and L_(2) are two lines on P_(1) and P_(2) respectivelym such that their intersection is the origin. Show that there exist points, A, B and C , whose perpmutation, A, B' and C' respectively, can be chosen such that (i) A is on L_(1) 'B and P_(1) " put not on " L_(1) and C not on P_(1) , (ii) A is on L_(2) , B' on P_(2) " but not on " L_(2) and C' " not on" P_(2) .
Answer» Solution :Fig A 2.29 shows the possi9ble sitution for PLANES`P_(1) and P_(2)` and the lines `L_(1) and L_(2)` : Now if we choss points A,B and C as A on `L_(1)` B on th3e LINE of interection of ` P_(1) and P_(2)`but other than th3 origin and C on `L_(2)` again other than the origin. then we can consider. a correspondes to one A', B', C' B corresponds to one of the REMAINING of A' B' and C' C corresponds to THRID of A', B', and C',e.g. A'= C' B = , C' =A Hence one permutation of [ A B C ] is [ C B A] . hence proved.