Planes
Equation of planes can expressed in either vector or cartesian form. Vector
equation is the one containing only vectors. Cartesian equation is in the form:
Contains a point and parallel to 2 vectors
Suppose a plane:
- is parallel to both
and where - contains
Equation for the plane is:
Contains a point and normal is given
Suppose a plane:
- contains
- has a normal
Equation for the plane is:
Contains 3 points
Suppose a plane contains
Normal to a plane
Suppose
Angle between 2 planes
Consider the two planes:
The angle between the planes
Here
Shortest distance to a point
Considering a plane
is a normal to the plane is the position vector of any known point on the plane is the position vector to the arbitrary point