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

Three lines $3x - y = 2$,$5x + ay = 3$,and $2x + y = 3$ are concurrent. Find the value of $a$.

If $k_{i}$ are possible values of $k$ for which lines $kx + 2y + 2 = 0$,$2x + ky + 3 = 0$,and $3x + 3y + k = 0$ are concurrent,then $\sum k_{i}$ has the value

For all values of $\theta$,the line $(2 \cos \theta + 3 \sin \theta) x + (3 \cos \theta - 5 \sin \theta) y - (5 \cos \theta - 2 \sin \theta) = 0$ passes through which fixed point?

The point of intersection of the lines joining points $\hat{i}+2 \hat{j}, 2 \hat{i}-\hat{j}$ and $-\hat{i}, 2 \hat{i}$ is

By using the concept of the equation of a line,prove that the three points $(3,0), (-2,-2),$ and $(8,2)$ are collinear.