Question

What is the point-normal form of the equation of a plane?

Answer 1

See below.

Explanation:

Given a fixed point

`p_0=(x_0,y_0,z_0)`

an a generic point

`p = (x,y,z)`

and a non null vector

`vec n = (n_x,n_y,n_z)`

the formulation `<< p-p_0, vec n >> = 0` with `<< cdot, cdot >>` representing scalar product, indicates the set of points including `p_0` that are orthogonal to the vector `vec n`.

We have also the long version as

`(x-x_0)n_x+(y-y_0)n_y+(z-z_0)n_z=0`