If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = \dots$

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 $(2, 3, c)$ 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) = $

The direction cosines of the line joining the points $(-2, 4, -5)$ and $(1, 2, 3)$ are

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

If $\left( \frac{1}{2}, \frac{1}{3}, n \right)$ are the direction cosines of a line,then the value of $n$ is