If a line makes an angle of $\frac{\pi}{3}$ with each $X$ and $Y$ axis,then the acute angle made by $Z$-axis is

If the line $\overrightarrow{OR}$ makes angles $\theta_{1}, \theta_{2}, \theta_{3}$ with the planes $XOY, YOZ, ZOX$ respectively,then $\cos ^{2} \theta_{1}+\cos ^{2} \theta_{2}+\cos ^{2} \theta_{3}$ is equal to

$A$ 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 the direction ratios $a, b, c$ of a line $L$ satisfy the relations $ab + bc + ca = 0$ and $6ab + 9bc + 8ca = 0$, then the direction cosines of the line $L$ are

If $\cos \alpha, \cos \beta, \cos \gamma$ are the direction cosines of a vector $\vec{a}$,then $\cos 2 \alpha + \cos 2 \beta + \cos 2 \gamma$ is equal to

If the direction cosines of two lines satisfy the equations $l-2m+n=0$ and $lm+10mn-2nl=0$,and $\theta$ is the angle between the lines,then $\cos \theta=$