Consider the lines given by : `L_1 : x+3y-5=0, L_2 : 3x-ky-1=0, L_3 : 5x+2y-12=0` If `a` be the value of `k` for which lines `L_1, L_2, L_3` do not form a triangle and `c` be the value of `k` for which one of `L_1, L_2, L_3` is parallel to at least one of the other lines, then `abc=`

Consider the lines give by L_1: x+3y -5=0, L_2:3x - ky-1=0, L_3: 5x +2y -12=0

L_(1)=x+3y-5=0,L_(2)=3x-ky-1=0,L_(3)=5x+2y-12=0 are concurrent if k=

Consider the lines given by L_(1):x+3y-5=0," "L_(2):3x-ky-1=0" "L_(3):5x+2y-12=0 {:(,"Column-I",,"Column-II"),((A),","L_(1)","L_(2)","L_(3)" are concurrent, if",(p),k=-9),((B)," One of "L_(1)","L_(2)","L_(3)" is parallel to at least one of the other two, if",(q),k=-6/5),((C),L_(1)","L_(2)","L_(3)" from a triangle, if",(r),k=5/6),((D),L_(1)","L_(2)","L_(3)" do not from a triangle, if",(s),k=5):}

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 the lines given by L_1 = x + 3y – 5 = 0 L_2 = 3x – ky – 1 = 0 L_3 = 5x + 2y – 12 = 0 Match the statements/Expression in Column-I with the statements/Expressions in Column-II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in OMR.

The area of triangle formed by the lines l_1 and l_2 and the x-axis is: