Question

Derive the equation of a plane in normal form (both in the vector and Cartesian form.)

Answer 1

If $n$ is a vector normal to a given plane, directed from the origin to the plane and $p$ is the length of the perpendicular drawn from the origin to the plane the the vector equation of the plane is $\overrightarrow{r}\cdot \overrightarrow{n}=p$

(In Cartesian form)

Let $a.b.c$ be three direction ratios of the normal to a given plane, and $p$ be the length of perpendicular drawn from the origin to the given plane, then the equation of plane is $ax+by+cz=p$.