Two planes` P_1 and P_2` pass through origin. Two lines `L_1 and L_2` also passingthrough 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:

Two planes P_(1) and P_(2) pass through origin. Two lines L_(1) and L_(2) also passingthrough 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]^(2) exists.Such that:

If lines l_(1), l_(2) and l_(3) pass through a point P, then they are called…………. Lines.

P_1 and P_2 are planes passing through origin L_1 and L_2 are two lines on P_1 and P_2, respectively, such that their intersection is the origin. Show that there exist points A ,B and C , whose permutation A^(prime),B^(prime)a n dC^(prime), respectively, can be chosen such that i) A is on L_1,B on P_1 but 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_2dot

Let L_1 and L_2 be two lines intersecting at P If A_1,B_1,C_1 are points on L_1,A_2, B_2,C_2,D_2,E_2 are points on L_2 and if none of these coincides with P, then the number of triangles formed by these 8 points is

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot