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 direction ratios of the line of intersection of the planes $x-y+z-5=0$ and $x-3 y-6=0$, are

The distance between the line $\overline{\mathrm{r}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$ and the plane $\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})=4$ is