If $\alpha, \beta$ and $\gamma$ are the angles which a half ray makes with the positive direction of the axes,then $\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma$ is equal to

The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

$A$ line $AB$ in three dimensions makes angles $45^{\circ}$ and $120^{\circ}$ with the positive $X$-axis and the positive $Y$-axis respectively. If $AB$ makes an acute angle $\theta$ with the positive $Z$-axis,then $\theta$ equals (in $^{\circ}$)

If the direction ratios $(l, m, n)$ of two lines satisfy the equations $l+m+n=0$ and $mn-2ln+lm=0$, then the angle between the lines is

If two straight lines whose direction cosines are given by the relations $l+m-n=0$ and $3l^{2}+m^{2}+cnl=0$ are parallel,then the positive value of $c$ is