# Planes in 3D

## General plane equation

$Ax+By+Cz=D$

## Normal to a plane

$\stackrel{\to }{n}=A\stackrel{\to }{i}+B\stackrel{\to }{j}+C\stackrel{\to }{k}$

## Plane by normal and point

Given $\stackrel{\to }{n}$ - normal and point $\stackrel{\to }{p}$ on the plane $Ax+By+Cz=D$
?if I got it right?

${n}_{1}\left(x-{p}_{1}\right)+{n}_{2}\left(y-{p}_{2}\right)+{n}_{3}\left(z-{p}_{3}\right)=0$

## Point distance to plane

Given a point $\stackrel{\to }{p}$ on the plane $Ax+By+Cz=D$
the distance $d$ from the point to the plane will be:

$d=\frac{A{p}_{1}+B{p}_{2}+C{p}_{3}-D}{\sqrt{{A}^{2}+{B}^{2}+{C}^{2}}}$