# If $O$ is origin, $|\overrightarrow{OP}|=3$ with $d.r.=(-1,2,-2)$ then the coordinate of $P$ is ?

$\begin{array}{1 1} (-1,2,-2) \\ (1,2,2) \\ (3,6,-9) \\ (\frac{-1}{9}, \frac{2}{9},\frac{-2}{9} ) \end{array}$

Given: $d.r.$ of $\overrightarrow{OP}=(-1,2,-2)$
$\Rightarrow\:P(-1,2,-2)$

Given origin O = (0, 0, 0) and $|\overrightarrow{OP}| = 3$
Direction ratios of $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} = 3$
\begin{align*}(i.e)\; \sqrt{(-1-0)^2 + (2-0)^2 + (-2-0)^2} &= 3 \\ \sqrt{1+4+4 }& = 3 \end{align*}
Hence the coordinate of P is (-1, 2, -2)