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 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 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 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 following lines : L_(1) : x-y-1=0 L_(2):x+y-5=0 L_(3):y-4=0 Let L_(1) is axis to a parabola, L_(2) is tangent at the vertex to this parabola and L_(3) is another tangent to this parabola at some point P. Let 'C' be the circle circumscribing the triangle formed by tangent and normal at point P and axis of parabola. The tangent and normals at normals at the extremities of latus rectum of this parabola forms a quadrilateral ABCD. Q. The equation of the circle 'C' is :

Consider the lines: L_1:(x-2)/1=(y-1)/7=(z+2)/-5, L_2:x-4=y+3=-z Then which of the following is/are correct ? (A) Point of intersection of L_1 and L_2 is (1,-6,3)

The shortest distance between the two lines L_1:x=k_1, y=k_2 and L_2: x=k_3, y=k_4 is equal to

Consider the lines L_(1) : x/3 +y/4 = 1 , L_(2) : x/4 +y/3 =1, L_(3) : x/3 +y/4 = 2 and L_(4) : x/4 + y/3 = 2 .Find the relation between these lines.

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

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),L_(3) be the lines of intersection of the planes P_(2) and P_(3),P_(3) and P_(1),P_(1) and P_(2) respectively. Statement I Atleast two of the lines L_(1),L_(2) and L_(3) are non-parallel. Statement II The three planes do not have a common point.