Vector Equations of Plane (평면의 벡터 방정식)

Plane equation with a point and a normal vector
In a three-dimensional space, another important way of defining a plane is by specifying a point and a normal vector to the plane.
Let $\textbf{r}_0$ be the position vector of some known point $P_0$ in the plane, and let $\textbf{n}$ be a nonzero vector normal to the plane. The idea is that a point $P$ with position vector $\textbf{r}$ is in the plane if and only if the vector drawn from $P_0$ to $P$ is perpendicular to $\textbf{n}$. Recalling that two vectors are perpendicular if and only if their dot product is zero, it follows that the desired plane can be expressed as the set of all points $\textbf{r}$ such that $\textbf{n} \cdot (\textbf{r}-\textbf{r}_0)=0$.