$A$ line which makes an angle of $60^o$ with the $y$-axis and $z$-axis,then the angle which it makes with the $x$-axis is ......... $^o$.

Suppose $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$ are the direction cosines of two lines and $\theta$ is the angle between them,where $\cos \theta = \pm(l_1 l_2 + m_1 m_2 + n_1 n_2)$. Let $A=(1, -2, 3)$,$B=(3, 1, -3)$,and $C=(-3, 1, 3)$ be the vertices of $\triangle ABC$. Then,$\cos A =$

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5)$,$B(-1, 3, 2)$,and $C(\lambda, 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes,then the value of $(\lambda^3 + \mu^3 + 5)$ is

The projection of the line segment joining the points $(-1, 0, 3)$ and $(2, 5, 1)$ on the line whose direction ratios are $6, 2, 3$ is

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

If a line makes angles of measure $\frac{\pi}{6}$ and $\frac{\pi}{3}$ with $X$ and $Y$ axes respectively,then the angle made by the line with $Z$ axis is