The plane

In space the plane becomes a geometric object with an equation of its own: it is identified by a point and by a normal vector $\vec n=(a,b,c)$, and has Cartesian equation $ax+by+cz+d=0$. Starting from planes one builds the pencils of planes: proper (all the planes through a line) and improper (all the planes parallel to a given plane).

• Equation of the plane
• Plane through three points
• Pencil of planes
• Proper pencil
• Improper pencil
• Thales in space