Consider three planes P₁: x-y+z=1, P₂: x+y-z=-1 and P₃: x-3 y+3 z=2 Let L₁, L₂ and L₃ be the lines of intersection of the planes P₂ and P₃, P₃ and P₁, P₁ and P₂ , respectively. Statement 1 Atleast two of the lines L₁, L₂ and L₃ are non-parallel. Statement 2 The three planes do not have a common point.

Step-by-step solution

The given equations are aligned & x-y+z=1, & x+y-z=-1 and x-3 y+3 z=2 aligned The system of equations can be put in matrix form as A X=B which is inconsistent as (A: B) (A) . The three planes do not have a common point. Statement 2 is true. Since, planes P₁, P₂ and P₃ are pairwise intersection, their lines of intersection are parallel. Statement 1 is false.