Consider the lines given by L₁: x+3 y-5=0, L₂: 3 x-k y-1=0, L₃: 5 x+2 y-12=0 Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Step-by-step solution

(A) Solving equations L₁ and L₃ , aligned x -36+10 & = y +12-25 = 1 2-15 x & =2, y=1 aligned L₁, L₂, L₃ are concurrent, if point (2,1) lies on L₂ . 6-k-1=0 k=5 (B) Either L₁ is parallel to L₂ , or L₃ is parallel to L₂ , then aligned & 1 3 = 3 -k or 3 5 = -k 2 & k=-9 or k=- 6 5 aligned k=-9 or k=- 6 5 (C) L₁, L₂, L₃ form a triangle, if they are not concurrent, or not parallel. k 5,-9,- 6 5 k= 5 6 (D) L₁, L₂, L₃ do not form a triangle, if k=5,-9,- 6 5