Given a line $L:\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$, then

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. The foot of perpendicular from point (1, 6, 3) on line L	I. $2\sqrt{13}$
B. Perpendicular distance from point (1, 6, 3) to line L	II. (1, 0, 7)
C. Image of point (1, 6, 3) with respect to line L	III. (1, 3, 5)
D. Distance between points (1, 6, 3) and (1, 0, 7)	IV. $\sqrt{13}$

Choose the correct answer from the options given below:

The shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and $\frac{x-2}{4} = \frac{y-4}{6} = \frac{z-5}{8}$ is equal to

The vector equation of the line joining the points $(-2, -3, -4)$ and $(1, -2, 4)$ is :

A line makes angle $\theta$ with $x$-axes as well as $z$-axis. If the angle $\beta$, which it makes with $y$-axis is such that $\sin^2\beta = 3\sin^2\theta$, then $\cos^2\theta$ is :

If two lines $\frac{x-3}{2} = \frac{y-4}{5} = \frac{z}{4}$ and $\frac{x-4}{3} = \frac{y-5}{6} = \frac{1-z}{k}$, are coplanar, then $k$ is equal to

Image of origin with respect to plane $x + y + z = 3$ is:

The coordinates of the image of the point P (5, 4, 2) in the line $\vec{r} = (-\hat{i} + 3\hat{j} + \hat{k}) + \mu(2\hat{i} + 3\hat{j} - \hat{k})$, where $\lambda$ is a parameter, is