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@@.