Planes

Question 1

When you have two planes what possible ways can they intersect

Answer 1

Same plane - infinity many solutions
Parallel planes - no solutions
Intersect with a common line - infinitely many solutions along a line

Question 2

When having three planes what are the many ways they can interact with

Answer 2

Same plane - infinity many solutions
2 planes the same one is parallel - no solutions
3 planes parallel - no solutions
2 parallel one intersecting both - no solutions
All three intersecting at one point - 1 solution
All three intersecting at line - sheaf - infinitely many solutions number of solutions
Triangular prism - no solutions

Question 3

When the determinant is not 0 what type of intersection do u have

Answer 3

3 planes intersecting at one point