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Intersection of Three 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.
c) For each case, write down:
  • 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