Question

If $OP=r,d.c^{\prime }s$ of $\overrightarrow{OP}$ are $l,m,n$ then $P=\pm (lr,mr,nr)$

Answer 1

Let $(x,y,z)$ be coordinates of $P$ and $A$ the foot of $\perp$ from $P$ on x axis

Then $x=OA$

Now $\frac{OA}{OP}=\cos \alpha$

$\therefore$ $OA=OP\cos \alpha =r\cos \alpha$

From (1)

$x=OA=r\cos \alpha =rl$

$y=mr,n=2r$

Thus coordinates of $P$ are $(lr,mr,nr)$