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 value of $\lambda$, so that the lines $\frac{1-x}{3} = \frac{7y-14}{2\lambda} = \frac{z-3}{2}$ and $\frac{7-7x}{3\lambda} = \frac{y-5}{1} = \frac{6-z}{5}$ are perpendicular is:

Distance between two planes $x + 2y - z = 5$ and $2x + 4y - 2z + 2 = 0$ is

Match List-I with List-II

Choose the correct answer from the options given below:

Match List-I with List-II

Choose the correct answer from the options given below:

Which of the following statements are correct?

(A) The angle between the vectors with direction ratios proportional to -3, 5, 4 and 4, 5, 3 is $\dfrac{\pi}{3}$

(B) The direction cosines of Y-axis is 0, 1, 0.

(C) The cartesian equation of a line is $3x-6=2y+1=2z-1$, then its direction ratios are proportional to 2, 2, 3

(D) The vector equation of the line passing through the point $(2,-1,-1)$ and direction ratios 1, 2, 3 is $\vec r=(2\hat i-\hat j-\hat k)+\lambda(\hat i+2\hat j+3\hat k)$

Choose the correct answer from the options given below:

The points on the line $\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2}$ at a distance of $\sqrt{17}$ from the point (-2, -1, 3) are: