00:01
So here we are asked kind of some general questions about line and plane intersections.
00:07
The first is how many ways can a line and a plane intersect, given that they do intersect.
00:17
And the answer to that, if you kind of think about it for a bit, throughout math, there are a few different ways systems of equations can behave.
00:26
There can be, or linear equations at least, there can be exactly one solution.
00:30
There can be no solution or there can be infinitely many solutions.
00:36
In the case where there is no solution, that would be like a line and a plane never intersecting at all.
00:44
And so if they do intersect, then there are only two different ways.
00:52
The case where there is exactly one solution to the system is the case where they intersect at a single point.
01:04
That would be like a line piercing the plane, which you could see maybe like this, maybe it comes from under the plane and then pierces through right at that point, and that point is the solution to the system.
01:29
Or if there are infinitely many solutions, the line lies on the plane where this line is just sitting in the exact same plane as the red object, and all of these points are infinitely many points of intersection.
02:06
Part b is asking us why it is only possible to either have one infinitely many or no intersections, why we can't have multiple intersections...