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

If a line makes angles $90^{\circ}, 60^{\circ}$ and $30^{\circ}$ with the positive direction of $x, y$ and $z$-axes respectively,find its direction cosines.

If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$, then $\beta$ is equal to

If a straight line in space is equally inclined to the coordinate axes,the cosine of its angle of inclination to any one of the axes is

Let $ABC$ be a triangle with vertices at points $A(2, 3, 5)$,$B(-1, 3, 2)$ and $C(\lambda, 5, \mu)$ in three-dimensional space. If the median through $A$ is equally inclined with the axes,then $(\lambda, \mu)$ is equal to

If the coordinates of the points $A, B, C, D$ are $(2, 3, -1), (3, 5, -3), (1, 2, 3)$ and $(3, 5, 7)$ respectively,then the projection of $AB$ on $CD$ is