Class 12MathematicsTHREE DIMENSIONAL GEOMETRYSystem of co-ordinates, Direction cosines and direction ratios, Projection
EasyIf the coordinates of a point $P$ with respect to the origin $O$ are $(3, 12, 4)$,then the direction cosines of $OP$ are ..........
- A$3, 12, 4$
- B$\frac{1}{4}, \frac{1}{3}, \frac{1}{2}$
- C$\frac{3}{\sqrt{13}}, \frac{1}{\sqrt{13}}, \frac{2}{\sqrt{13}}$
- D$\frac{3}{13}, \frac{12}{13}, \frac{4}{13}$
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If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is
DifficultAP EAMCET 2021
View SolutionThe direction cosines of the line making angles $\frac{\pi}{4}, \frac{\pi}{3}$ and $\theta$ $(0 < \theta < \frac{\pi}{2})$ respectively with $X, Y$ and $Z$ axes are:
The direction cosines of the line passing through $P(2, 3, -1)$ and the origin $O(0, 0, 0)$ are:
If a line makes an angle of $\frac{\pi}{3}$ with each of the $X$ and $Y$-axes,then the acute angle made by the line with the $Z$-axis is:
The angle between two lines whose direction ratios are $(1, 1, 2)$ and $(\sqrt{3} - 1, -\sqrt{3} - 1, 4)$ is ......... $^o$.
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