The distance between the parallel lines $$\frac{x-2}{3}=\frac{y-4}{5}=\frac{z-1}{2}$$ and $$\frac{x-1}{3}=\frac{y+2}{5}=\frac{z+3}{2}$$ is

The coordinates of the foot of the perpendicular drawn from the origin to the plane $$2 x+y-2 z=18$$ are

The vector equation of the line passing through $$\mathrm{P}(1,2,3)$$ and $$\mathrm{Q}(2,3,4)$$ is

Equation of planes parallel to the plane $$x-2y+2z+4=0$$ which are at a distance of one unit from the point (1, 2, 3) are