If  O is the origin and the line OP of length r makes an angle α  with x- axis and lies in the xz- plane, then the coordinates of P are

# If  $O$ is the origin and the line $OP$ of length $r$ makes an angle $\alpha$  with $x-$ axis and lies in the $xz-$ plane, then the coordinates of $P$ are

1. A

$\left(0,0,r\mathrm{sin}\alpha \right)$

2. B

$\left(\mathrm{cos}\alpha ,0,0\right)$

3. C

$\left(r\mathrm{cos}\alpha ,r\mathrm{sin}\alpha ,0\right)$

4. D

$\left(r\mathrm{cos}\alpha ,0,r\mathrm{sin}\alpha \right)$

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### Solution:

If a $P$ point lines on the $xz-$plane then the coordinates of the point  $P$ can be taken as$\left(x,0,z\right)$

Given the angle made by the line with  $x-$axis is  and the $\alpha$ angle made by the same line with $z-$ axis is  $90°-\alpha$

Therefore, the coordinates of the point $P\overline{)\left(r\mathrm{cos}\alpha ,0,r\mathrm{sin}\alpha \right)}$

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