The angle between a line with direction ratios $2 : 2 : 1$ and a line joining $(3, 1, 4)$ to $(7, 2, 12)$ is

If $\frac{x - 1}{l} = \frac{y - 2}{m} = \frac{z + 1}{n}$ is the equation of the line passing through the points $(1, 2, -1)$ and $(-1, 0, 1)$,then the direction ratios $(l, m, n)$ are:

If the shortest distance between the lines $\frac{x-\lambda}{2}=\frac{y-4}{3}=\frac{z-3}{4}$ and $\frac{x-2}{4}=\frac{y-4}{6}=\frac{z-7}{8}$ is $\frac{13}{\sqrt{29}}$,then a value of $\lambda$ is :

The equation of the line passing through the points $(3, 2, 4)$ and $(4, 5, 2)$ is

The equation of the line passing through the point $(1, -3, 5)$ and making equal angles with the coordinate axes is:

Find the foot of the perpendicular from the point $(2, 3, -8)$ to the line $\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}$. Also,find the perpendicular distance from the given point to the line.