The projections of a line segment on the $x, y, z$ axes are $12, 4, 3$ respectively. Find the length and the direction cosines of the line segment.

Consider the following statements:
Assertion $(A)$: The direction ratios of a line $L_1$ are $2, 5, 7$ and the direction ratios of another line $L_2$ are $\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. Then the lines $L_1, L_2$ are parallel.
Reason $(R)$: If the direction ratios of a line $L_1$ are $a_1, b_1, c_1$, the direction ratios of a line $L_2$ are $a_2, b_2, c_2$ and $a_1 a_2 + b_1 b_2 + c_1 c_2 = 0$, then the lines $L_1, L_2$ are parallel. Which one of the following is true?

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is

$A$ line makes an angle $\theta$ with the $X$ and $Z$ axes and an angle $\beta$ with the $Y$ axis. If $\sin^2 \beta = 3 \sin^2 \theta$,then $\cos^2 \theta = \dots$

In three-dimensional space,a line $AB$ makes angles of $45^\circ$ and $120^\circ$ with the positive $x$-axis and $y$-axis,respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$-axis,then $\theta = \dots^\circ$.

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is