$A$ vector makes equal angles $\alpha$ with $x$ and $y$ axes and $90^{\circ}$ with $z$-axis. Then $\alpha=$

If the direction ratios $a, b, c$ of a line $L$ satisfy the relations $ab + bc + ca = 0$ and $6ab + 9bc + 8ca = 0$, then the direction cosines of the line $L$ are

Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ are $.......$

The angle between the lines whose direction ratios are proportional to $(1, 2, 1)$ and $(2, -3, 6)$ is

$\text{Assertion (A)}$: 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

If a line makes angles of $30^o$ and $45^o$ with $X-$ axis and $Y-$ axis,then the angle made by it with $Z-$ axis is