Consider three planes `P_1 : x-y + z = 1`, `P_2 : x + y-z=-1` and `P_3 : x-3y + 3z = 2` Let `L_1, L_2` and `L_3` be the lines of intersection of the planes `P_2 and P_3`, `P_3 and P_1` and `P_1 and P_2` respectively.Statement 1: At least two of the lines `L_1, L_2 and L_3` are non-parallel The three planes do not have a common point

Consider three planes P_(1):x-y+z=1 P_(2):x+y-z=-1 and " "P_(3):x-3y+3z=2 Let L_(1),L_(2),L_(3) be the lines of intersection of the planes P_(2) and P_(3),P_(3) and P_(1),P_(1) and P_(2) respectively. Statement I Atleast two of the lines L_(1),L_(2) and L_(3) are non-parallel. Statement II The three planes do not have a common point.

Consider three planes p _(1): x-y+z=1, p _(1)P: x + y-z=-1 and p _(3) :x - 3y+ 3z =2. Let I_(1), I _(2), I _(3) the lines of intersection of the planes P _(2)and P _(3) , P _(3) and P _(1), P _(1) and P _(2), respectively. Statement I : Atleast two of the lines I_(1), I_(2) are non-parallel. Statement II : The three planes do not have a common point. For the following question, choose the correct answer from the codes (A), (B), (C ) and (D) defined as follows.

Consider three planes P_1:x-y+z=1, P_2:x+y-z=-1,P_3,x-3y+3z=2 Let L_1,L_2,L_3 be the lines of intersection of the planes P_2 and P_3 and P-1,P_1 and P_2, respectively.

Consider the planes p _(1) : 2x + y+ z+4=0 p _(2) :y -z+4 =0 and p _(3) : 3x+ 2y +z+8=0 Let L_(1),I _(2), I_(3) be the lines of intersection of the planes P_(2)and P_(3), P_(3) and P _(1),P_(1) and P _(2) respectively. Then:

Consider the three planes P_1 :3x +15 y +21 z=9 , P_2 :x - 3y -z=5 , and P_3 : 2x +10y +14 z =5 then , which one of the following is true ?

Let P_(1) : 2x + y + z + 1 = 0 P_(2) : 2x - y + z + 3 = 0 and P_(3) : 2x + 3y + z + 5 = 0 be three planes, then the distance of the line of intersection of planes P_(1) = 0 and P_(2) = 0 from the plane P_(3) = 0 is

Let L.be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2. If L makes an angles alphawith the positive x-axis, then cos alpha equals