If a line makes angles $90^{\circ}, 60^{\circ}$ and $\theta$ with $x, y$ and $z$ axes respectively,where $\theta$ is acute,then the value of $\theta$ is

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

Find the direction cosines of the vector joining the points $A(1, 2, -3)$ and $B(-1, -2, 1)$,directed from $A$ to $B$.

$A$ line makes the same angle $\theta$ with each of the $x$ and $z$ axes. If the angle $\beta$ which it makes with the $y$-axis is such that $\sin^2 \beta = 3\sin^2 \theta$,then $\cos^2 \theta$ is-

$A$ 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 ......... $^o$.

If a variable line in two adjacent positions has direction cosines $l, m, n$ and $l+\delta l, m+\delta m, n+\delta n,$ show that the small angle $\delta \theta$ between the two positions is given by $\delta \theta^{2}=\delta l^{2}+\delta m^{2}+\delta n^{2}$.