Equation of a Plane
Couple sections ago, we saw that the equation of plane can be expressed as
. However, this equation does not give much information. So suppose we have the following graph:
are position vectors for points
is a normal vector that is orthogonal (perpendicular) to the plane.
is on the plane, then
is orthogonal to
. In other words, their dot products should give 0.
Which is formula for the equation of a plane.
The key to finding the equation of a plane is finding two things:
- The normal vector (orthogonal to the plane)
- A point on the plane.
Then you can just plug those into the formula to get the equation!