The line passing through the point $(5,1, a)$ and $(3, \mathrm{~b}, 1)$ crosses the $y \mathrm{z}$-plane at $\left(0, \frac{17}{2}, \frac{-13}{2}\right)$, then the value of $2 a+3 b$ is

The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices are lie on the line $y=2 x+\mathrm{c}$ where c is the constant, then co-ordinates of other two vertices are

The joint equation of the bisectors of the angles between the lines $x=5$ and $y=3$ is

If the line $2 x+y=\mathrm{k}$ passes though the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ internally in the ratio $3: 2$ then, $(k+1):(k-1)=$