Proof of the shortest distance from a point to a plane formula?
How can you prove that, for a plane with equation ax+bx+cz=d and a point (alpha, beta, gamma) the shortest distance from the point to the plane is given by
(aalpha+b beta+cgamma-d)/sqrt(a^2+b^2+c^2)
How can you prove that, for a plane with equation
1 Answer
Quite easy.
Given the plane
with
and the point
is normal by construction to
The intersection point
and now the sought distance is given by