Direction cosines of 2 lines are given by the equations $3l+m+5n=0, 6mn-2nl+5lm=0$ then which of the following statements are correct ?

(A) Direction ratios of two lines are (1, 2, -1) and (-2, 1, 1).

(B) Angle between lines is $\frac{\pi}{3}$.

(C) The angle between the lines is $\cos^{-1}\left(-\frac{1}{6}\right)$.

(D) Vectors parallel to these lines are $\hat i+2\hat j-\hat k$ and $-2\hat i+\hat j+\hat k$.

Choose the correct answer from the options given below:

The angle between the line $2x = 3y = z$ and $x$- axis is:

Consider the lines $l_1: \frac{x-1}{0} = \frac{y-1}{1} = \frac{2-z}{1}$ and $l_2: \frac{x}{2} = \frac{y}{0} = \frac{2z-1}{4}$, then which of the following are correct?

(A) Direction Ratio's of $l_1 = <0, 1, 1>$

(B) Direction Ratio's of $l_2 = <2, 0, 2>$

(C) Angle between $l_1$ and $l_2 =$ $\frac{\pi}{3}$

(D) Angle between $l_1$ and $l_2 =$ $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

The shortest distance between the lines $\vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} - \hat{j} + \hat{k})$ and $\vec{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu(4\hat{i} - 2\hat{j} + 2\hat{k})$ is

If the lines $\frac{x-1}{2} = \frac{y-m}{3} = \frac{z-3}{4}$ and $\frac{x-4}{5} = \frac{y-1}{2} = z$ are interesecting, then the value of $m$, is

Equation of y-axis in space, in vector form is :

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is :