Match the LIST-I with LIST-II

	LIST-I (Equation of Line)		LIST-II (Direction Ratio of line)
A.	$\dfrac{2-x}{1} = \dfrac{2y+1}{1} = \dfrac{z}{1}$	I.	$2, 1, 1$
B.	$x = 2y+3,\ z = y+1$	II.	$1, -2, 2$
C.	$\dfrac{x-1}{1} = \dfrac{y+1}{2},\ z = 1$	III.	$-2, 1, 2$
D.	$\vec{r} = \hat{i} + \hat{j} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k})$	IV.	$1, 2, 0$

Choose the correct answer from the options given below:

If a line makes angles 90 degree, 60 degree and $\theta$ with $x, y$ and $z$ axis respectively, where $\theta$ is acute, then value of $\theta$ is:

The distance of the plane $\vec{r} \cdot \left(\frac{2}{7}\hat{i} + \frac{3}{7}\hat{j} - \frac{6}{7}\hat{k}\right) = 2$ from the origin is

If the shortest distance between the lines $\vec r=(\hat i+2\hat j+3\hat k)+\lambda(2\hat i+3\hat j+4\hat k)$ and $\vec r=(a\hat i+4\hat j+5\hat k)+\mu(4\hat i+6\hat j+8\hat k)$, $a \in N$, where $\lambda$ and $\mu$ are parameters, is $\sqrt{\dfrac{5}{29}}$, then $a$ is equal to

The shortest distance between the lines $\frac{x+3}{1} = \frac{y-2}{2} = \frac{z+4}{3}$ and $\frac{x+3}{-3} = \frac{y+7}{2} = \frac{z-6}{4}$ is :

The value of $\lambda$ so that the lines $\dfrac{1-x}{3} = \dfrac{7y-14}{2\lambda} = \dfrac{z-3}{2}$ and $\dfrac{7-7x}{3\lambda} = \dfrac{y-5}{1} = \dfrac{6-z}{5}$

are at right angles is:

If the direction ratios of two lines are $a, b, c$ and $(b-c), (c-a), (a-b)$ respectively, then the angle between these lines is: