Find the direction cosines of $x$,$y$,and $z$-axis.

If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes and $\cos \alpha = 14/15, \cos \beta = 1/3$,then $\cos \gamma = \dots$

If a line makes angles $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive $X, Y$ and $Z$ axis respectively,then its direction cosines are

If the direction ratios of a line are $1, 1, 2$,find the direction cosines of the line.

In three-dimensional space,a line $AB$ makes angles of $45^\circ$ and $120^\circ$ with the positive $x$-axis and $y$-axis,respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$-axis,then $\theta = \dots^\circ$.

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