# Intersection of Three Planes

- Author:
- Kathryn Peake, Andreas Lindner

- Topic:
- Intersection, Planes

The following three equations define three planes:

**Exercise**a) Vary the sliders for the coefficient of the equations and watch the consequences. b) Adjust the sliders for the coefficients so that- two planes are parallel, the third plane intersects the other two planes,
- three planes are parallel, but not coincident,
- all three planes form a cluster of planes intersecting in one common line (a sheaf),
- all three planes form a prism,
- the three planes intersect in a single point.

- the equations,
- the matrix form of the system of equations, determinant, inverse matrix (if it exists)
- the equations of any lines of intersection
- any observations you make

Andreas Lindner