$A$ 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 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 $\alpha, \beta, \gamma$ are the angles made by a line with the positive directions of the $x, y, z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = \dots$

$A$ 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 $\cos^2 \theta$ equals:

If a unit vector $\vec{r}$ makes angles $\frac{\pi}{3}$ with $\hat{i}$,$\frac{\pi}{4}$ with $\hat{j}$ and $\theta \in (0, \pi)$ with $\hat{k}$,then a value of $\theta$ is

$E(1,0,0), F(0,2,0), G(0,0,3)$ are respectively the mid-points of the sides $AB, BC, CA$ of $\triangle ABC$. If $a_1, b_1, c_1$ and $a_2, b_2, c_2$ are respectively the direction ratios of $AF$ and $BG$, then $\frac{a_1^2+b_1^2+c_1^2}{a_2^2+b_2^2+c_2^2}=$