From the following options, the nearest line to the origin is ….

If the pair of straight lines $x y-x+y-1=0$ and the line $x+\mathrm{k} y-3=0$ are concurrent, then the value of $k$ is equal to

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