The direction cosines of a line are $\langle \frac{-9}{11}, \frac{6}{11}, \frac{-2}{11} \rangle$ respectively. Then its direction ratios are

Write the direction ratios of the vector $\vec{a} = \hat{i} + \hat{j} - 2\hat{k}$ and hence calculate its direction cosines.

If the direction cosines of a line are $\frac{1}{c}, \frac{1}{c}, \frac{1}{c}$,then:

If the relation between the direction ratios of two lines in $\mathbb{R}^3$ are given by $l+m+n=0$ and $2lm+2mn-ln=0$, then the angle between the lines is ($l, m, n$ have their usual meaning).

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 a line makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the $X$-axis and $Y$-axis respectively,then the angle made by the line with the $Z$-axis is