If $a, b, c$ are the direction ratios of a line $L$ and $\ell, m, n$ are its direction cosines,then $\frac{a^2}{b^2+c^2}=$

If a line makes angles of $120^{\circ}$ and $60^{\circ}$ with the $x$ and $y$ axes respectively,what angle does it make with the $z$ axis?

If $\alpha, \beta, \gamma$ are the direction angles of a vector and $\cos \alpha = \frac{14}{15}$,$\cos \beta = \frac{1}{3}$,then $\cos \gamma = $

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,$\cos A =$

Find the angle between the lines whose direction cosines are given by the equations $l+m+n=0$ and $l^{2}+m^{2}-n^{2}=0$.

If $OA$ is equally inclined to $OX, OY$ and $OZ$ and if $A$ is $\sqrt{3}$ units from the origin, then $A$ is: