Find the intersection of a line formed by the intersection of two planes $\overrightarrow{r}.{\overrightarrow{n}}_{1}={p}_{1}$ and $\overrightarrow{r}.{\overrightarrow{n}}_{2}={p}_{2}$

I know that the line would be along $({\overrightarrow{n}}_{1}\times {\overrightarrow{n}}_{2})$. So i need a point on the line to get the equation. I assumed a point C such that $\overrightarrow{OC}$ is perpendicular to the line of intersection. I dont really know how to proceed from here. Do I have to use the equations $\overrightarrow{c}.{\overrightarrow{n}}_{1}={p}_{1}$ and $\overrightarrow{c}.{\overrightarrow{n}}_{2}={p}_{2}$?

I know that the line would be along $({\overrightarrow{n}}_{1}\times {\overrightarrow{n}}_{2})$. So i need a point on the line to get the equation. I assumed a point C such that $\overrightarrow{OC}$ is perpendicular to the line of intersection. I dont really know how to proceed from here. Do I have to use the equations $\overrightarrow{c}.{\overrightarrow{n}}_{1}={p}_{1}$ and $\overrightarrow{c}.{\overrightarrow{n}}_{2}={p}_{2}$?