If the foot of the perpendicular drawn from the origin to a plane is $\mathrm{P}(2,-1,4)$, then the equation of the plane is

Let the plane passing through point $(2,1,-1)$ containing line joining the points $(1,3,2)$ and $(1,2,1)$ makes intercepts $\mathrm{p}, \mathrm{q}, \mathrm{r}$ on co-ordinate axes, then $\mathrm{p}+\mathrm{q}+\mathrm{r}=$

The angle between the line $x=\frac{y-1}{2}=\frac{z-3}{\lambda}$ and the plane $x+2 y+3 z=6$ is $\cos ^{-1} \sqrt{\frac{5}{14}}$, then the value of $\lambda$ is

The equation of the line passing through the point of intersection of $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-4}{5}=\frac{y-1}{2}=z$ and also through the point ( $2,1,-2$ ) is