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

Find the direction cosines and the length of a vector whose projections on the coordinate axes are $6, -3, 2$.

The perpendicular distance of the point $P(6, 7, 8)$ from the $XY$-plane is:

If the coordinates of the points $P, Q, R, S$ are $(1, 2, 3), (4, 5, 7), (-4, 3, -6)$ and $(2, 0, 2)$ respectively,then:

$\text{Assertion (A)}$: 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

The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is