What are the direction cosines of a line perpendicular to the $yz$-plane?

If the angle between the lines whose direction ratios are $4, -3, 5$ and $3, 4, k$ is $\frac{\pi}{3}$,then $k=$

If $(2, 3, c)$ are the direction ratios of a ray passing through the point $C(5, q, 1)$ and also the midpoint of the line segment joining the points $A(p, -4, 2)$ and $B(3, 2, -4)$,then $c \cdot (p + 7q) = $

$A$ line makes angles $\alpha, \beta, \gamma$ with the coordinate axes. If $\alpha + \beta = 90^o$,then $\gamma = $ ......... $^o$

If $\theta$ is the angle between the lines whose direction cosines $(l, m, n)$ satisfy the equations $6mn - 2nl + 5lm = 0$ and $3l + m + 5n = 0$,then $\sin \theta = $

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