The angle between the lines

$l_1: \frac{x + 1}{1} = \frac{2 - y}{2} = \frac{z - 1}{1}$ and $l_2: \frac{x - 1}{4} = \frac{2y - 4}{6} = \frac{z - 1}{2}$ is

Which of the following statements is/are TRUE?

(A) The angle between the lines whose direction ratios are proportional to (4, -3, 5) and (3, 4, 5) is 60°.

(B) If A(1,2,3) and B(2, 0, 5) are two points on a line, then its direction ratios are proportional to 1, -2, 2.

(C) The direction cosines of z-axis are 0, 0, 1.

(D) The vector equation of a line which passes through the point with position vector $3\hat{i}-\hat{j}+\hat{k}$ and is in the direction of $2\hat{i}+3\hat{j}+\hat{k}$ is $\vec{r} = (2\hat{i}+3\hat{j}+\hat{k}) + \lambda(3\hat{i}-\hat{j}+\hat{k})$, where $\lambda$ is a parameter.

Choose the correct answer from the options given below:

The distance of plane $\vec{r}\cdot(6\hat{i} - 3\hat{j} - 2\hat{k}) + 1 = 0$ from origin is :

If the two lines given by

$x=py+q, z=ry+s$ and

$x=p'y+q', z=r'y+s'$

are perpendicular, then which of the following is equal to -1 ?

If a line makes angles α, β and γ with positive x-axis, y-axis and z-axis respectively, then the value of

$sin^2\frac{α}{2}cos^2\frac{α}{2} + sin^2\frac{β}{2}cos^2\frac{β}{2} + sin^2\frac{γ}{2}cos^2\frac{γ}{2}$ is

The shortest distance between lines whose vector equations are: $\vec{r} = (1-t)\hat{i} + (t-2)\hat{j} + (3-2t)\hat{k}$ and $\vec{r} = (s+1)\hat{i} + (2s-1)\hat{j} - (2s+1)\hat{k}$, is:

The reflection of the point $(\alpha, \beta, \gamma)$ in the xz plane is