If lines represented by $x+3y-6=0$,$2x+y-4=0$ and $kx-3y+1=0$ are concurrent,then the value of $k$ is

If $\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix} = 0$,then the lines $a_i x + b_i y + c_i = 0$ $(i = 1, 2, 3)$ represent:

If the lines $L_1 \equiv x-2y+3=0$,$L_2 \equiv 2x+y+1=0$,and $L_3 \equiv 3x+y+c=0$ are concurrent and $\theta$ is the acute angle between the lines $L_1=0$ and $L_3=0$,then $\tan \theta=$

The points $A(1, 2)$,$B(2, 4)$,and $C(4, 8)$ form a/an

The line on which the lines $ax + by = 1$ and $bx + ay = 1$ (with $a \neq 0 \neq b$) intersect for any real values of $a$ and $b$ is

If the lines $x + 2ay + a = 0$,$x + 3by + b = 0$,and $x + 4cy + c = 0$ are concurrent,then $a, b,$ and $c$ are in which of the following?