What are the direction ratios of the line represented by the equations $x = ay + b$ and $z = cy + d$?

For what value of $\lambda$ are the lines $\frac{x - 1}{1} = \frac{y - 2}{\lambda} = \frac{z + 1}{-1}$ and $\frac{x + 1}{-\lambda} = \frac{y + 1}{2} = \frac{z - 2}{1}$ perpendicular to each other?

If a point $R(4, y, z)$ lies on the line joining the points $P(2, -3, 4)$ and $Q(8, 0, 10)$,then the distance of $R$ from the origin is

The shortest distance between the lines $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1}$ and $\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}$ is

The Cartesian equation of the line which is parallel to the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ and passing through the point $(1, -3, 5)$ is:

The shortest distance between the lines $x+1=2y=-12z$ and $x=y+2=6z-6$ is