First slide

Direction ratios and direction cosines

Question

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

Moderate

A

$(0, 0, r \sin α)$
B

$(\cos α, 0, 0)$
C

$(r \cos α, r \sin α, 0)$
D

$(r \cos α, 0, r \sin α)$

Solution

If a $P$ point lines on the $x z -$ plane then the coordinates of the point $P$ can be taken as $(x, 0, z)$
Given the angle made by the line with $x -$ axis is and the $α$ angle made by the same line with $z -$ axis is $90 ° - α$
Therefore, the coordinates of the point $P (r \cos α, 0, r \sin α)$

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