If $\alpha, \beta, \gamma$ are the angles made by a line with the positive directions of the $x, y, z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = \dots$

The direction cosines of the line $\frac{x-1}{0}=\frac{y+1}{5}=\frac{z-3}{0}$ are . . . . . . .

$A$ 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 $\cos^2 \theta = \dots$

Write the direction ratios of the vector $\vec{a} = \hat{i} + \hat{j} - 2\hat{k}$ and hence calculate its direction cosines.

The direction cosines of the line making angles $\frac{\pi}{4}, \frac{\pi}{3}$ and $\theta$ $(0 < \theta < \frac{\pi}{2})$ respectively with $X, Y$ and $Z$ axes are:

$\text{Assertion (A)}$: The direction ratios of line $L_1$ are $2, 5, 7$ and those of line $L_2$ are $\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. The lines $L_1, L_2$ are parallel.
$\text{Reason (R)}$: The direction ratios of a line $L_1$ are $a_1, b_1, c_1$ and those of another line $L_2$ are $a_2, b_2, c_2$. The lines $L_1$ and $L_2$ are parallel if $a_1 a_2+b_1 b_2+c_1 c_2=0$.
The correct option among the following is