`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)` .

Explanation

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.