If $< a, b, c >$ and $< a', b', c' >$ are the direction ratios of two perpendicular lines,then which of the following is true?

If a line makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the positive $x$ and $y$-axes respectively,then the angle made by the line with the positive $z$-axis is

The coordinates of a point $P$ are $(3, 12, 4)$ with respect to origin $O$. Find the direction cosines of $OP$.

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

If the coordinates of a point $P$ with respect to the origin $O$ are $(3, 12, 4)$,then the direction cosines of $OP$ are ..........

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