Collinearity of Three Points

Find the value of $k$, if the points $A(-2,3),B(1,2)$ and $C(k,0)$ are collinear.

If the points $\left(1,0\right),\left(0,1\right)$ and $\left(x,8\right)$ are collinear, then the value of $x$ is equal to

The points $\left(0,\frac{8}{3}\right),\left(1,3\right)$ and $\left(82,30\right)$

If the points $(-l,0)(0,m)$ and $(1,1)$ are collinear then the value of $\frac{1}{l}-\frac{1}{m}$ is

Find a relation between $x$ and $y$ if the points $(x, y)$,$(-1, 2)$and $(2, -3)$ are collinear.

If $P\equiv \left(\frac{1}{x_p},p\right); Q=\left(\frac{1}{x_q},q\right); R\equiv \left(\frac{1}{x_r},r\right)$ where $x_k\ne 0$, denotes the $k^{\mathrm{th}}$ terms of a $\mathrm{H}.\mathrm{P}.$ for $k\in N$, then :