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

1 Answer
Nov 10, 2016

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#