How to find the equation of the projective plane

How to find the projective plane equation:

For a point P0 = (x0, y0, z0) and a vector n = (a, b, c).

The plane equation is ax+by+cz=axbycz0.

This is the plane passing through point P0 and perpendicular to vector n.

Here P0 is the origin 0 (0, 0, 0), and the vector n is OP = (2, 9, -6).

So the plane equation is 2x+9y-6z=0.

Projective geometry

Projective geometry is a branch of geometry that studies the projective properties of figures, that is, they remain unchanged after projective transformations. Once also called projective geometry, projective geometry occupies a special position in classical geometry through which it can connect some other geometries.

Projective coordinates: Here we mainly introduce the projective coordinate system on a plane with points as basic elements. The projective coordinate systems on other two-dimensional basic shapes or basic shapes in other dimensions are similar to this. There are many methods to establish a projective coordinate system. Generally speaking, there are geometric methods and analytical methods.