If a line lies in the octant $OXYZ$ and it makes equal angles with the axes,then

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 $\alpha, \beta$ 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

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

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is

Let $A, B, C$ be three points on $\overline{OX}, \overline{OY}, \overline{OZ}$ respectively at distances $3, 6, 9$ from the origin $O(0, 0, 0)$. Let $Q$ be the point $(2, 5, 8)$ and $P$ be the point equidistant from $O, A, B, C$. Then,the coordinates of the point $R$ which divides $PQ$ in the ratio $3:2$ is