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If a line OP oflength $\mathrm{r}$ (where ' $\mathrm{O}$ ' is the origin) makes an angle $\alpha$ with $\mathrm{x}$ -axis and lies in the $\mathrm{xz}$ -plane, then what are the coordinates of $\mathrm{P} ?$
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The correct answer is:
$(r \cos \alpha, 0, r \sin \alpha)$
Since line OP of length 'r'which makes an angle ' $\alpha$ ' with $\mathrm{x}$ -axis lies in $\mathrm{xz}$ -plane. Therefore y-coordinate of $\mathrm{P}$ is zero. Now, from $\Delta \mathrm{OAP}$, we have $\mathrm{OA}=\mathrm{r} \cos \alpha, \mathrm{PA}=\mathrm{r} \sin \alpha$
$\therefore \quad \mathrm{P}=(\mathrm{r} \cos \alpha, 0, \mathrm{r} \sin \alpha)$
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