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Here is one option: 2 points uniquely define a line so a line can be named after any two points that belong to it. Similarly, three points that are not collinear (all in the same line) uniquely define a plane so a plane can be defined by naming any three non-collinear points in it.
There are different - though related - forms in coordinate geometry or in vector algebra.
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Name a plane that is not contained in plane n?
name a line that is not contained in plane N.
What is the name of a line that intersects a plane?
a line
What do you called an any closed plane made of line segments?
A plane shape. There is no specia name unless all the line segments are straight.
How come two points are not enough to name a plane?
Because a place can rotate around those two points as long as the line in on the plane. Two points defines a line. A plane requires 3 points.
When does a plane and line intersect at one point?
When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.
