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 given by L_(1):x+3y-5=0 L_(2):3x-ky-1=0 L_(3):5x+2y-12=0 Match the following lists.

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

Consider the lines given by L_1: x+3y-5=0 L_2:3x-k y-1=0 L_3:5x+2y-12=0 Column I|Column II L_1,L_2,L_3 are concurrent if|p. k=-9 One of L_1,L_2,L_3 is parallel to at least one of the other two if|q. k=-6/5 L_1,L_2,L_3 form a triangle if|r. k=5/6 L_1,L_2,L_3 do not form 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 . Statement 2:The three planes do not have a common point

Let L be the set of all lines in X Y=p l a n e and R be the relation in L defined as R={(L_1,L_2): L_1 is parallel to L_2}dot Show that R is an equivalence relation. Find the set of all lines related to the line y=2x+4.

Let L be the set of all lines in X Y=p l a n e and R be the relation in L defined as R={(L_1,L_2): L_1 is parallel to L_2}dot Show that R is an equivalence relation. Find the set of all lines related to the line y=2x+4.

Consider three lines as follows. L_1:5x-y+4=0 L_2:3x-y+5=0 L_3: x+y+8=0 If these lines enclose a triangle A B C and the sum of the squares of the tangent to the interior angles can be expressed in the form p/q , where pa n dq are relatively prime numbers, then the value of p+q is (a) 500 (b) 450 (c) 230 (d) 465

Consider three lines as follows. L_1:5x-y+4=0 L_2:3x-y+5=0 L_3: x+y+8=0 If these lines enclose a triangle A B C and the sum of the squares of the tangent to the interior angles can be expressed in the form p/q , where pa n dq are relatively prime numbers, then the value of p+q is

Let L be the set of all lines in X Y -plane and R be the relation in L defined as R={(L_1, L_2): L_1 is parallel to L_2} . Show that R is an equivalence relation. Find the set of all lines related to the line y=2x+4 .