The intersection of 2 non-parallel planes is always a line.
The intersection of 3 planes doesn't have to be a line, but it can be. If it is,
then there are an infinite number of other planes that can also intersect those
three along the same line.
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There are 3 planes of symmetry in a rectange.
A cube has three planes of symmetry.
They could line up in 3! = 3*2*1 = 6 ways.
If you were to have 3 points on the same line, then you would actually not be determining a plane, because there are infinitely many planes that can intersect a given line. But if you have 3 points in the form of the points (or vertices) of a triangle, then you determine a plane in the sense that there is only one possible plane upon which that triangle can be drawn (not including a degenerate triangle, which is equivalent to a line).
The intersection of the first and second quadrant on a Cartesian plane is null because the first quadrant consists of points with positive x and y coordinates, while the second quadrant consists of points with negative x and positive y coordinates. There are no points that satisfy both conditions simultaneously, resulting in an empty intersection. This is due to the nature of the coordinate system and the definitions of the quadrants based on the signs of the coordinates.