WOLFRAM|DEMONSTRATIONS PROJECT

Equation of a Plane

​
normal vector n = <a, b, c>
​
a
3
b
-2
c
4
initial point P = <
x
0
, y
0
, z
0
>
​
x
0
0
y
0
0
z
0
0
Given a fixed point
P
0
and a nonzero vector
n
, the set of points
P
in
3

for which
P
0
P
is orthogonal to
n
is a plane. The plane passing through the point
(
x
0
,
y
0
,
z
0
)
with normal vector
n=<a,b,c>
is described by the equation
a(x-
x
0
)+b(y-
y
0
)+c(z-
z
0
)=0
. This Demonstration shows the result of changing the initial point or the normal vector.