In Euclidean geometry, they can only intersect in 0, 1 or infinitely many points. If there are two points of intersection then the whole line lies in the plane.
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Yes, any points that are located on the same line will also be on the same plane. You can have more than one plane intersect a given line, but any points on that line will necessarily be on all the planes that intersect that line.
There are two possible answers; if the line is crossing the plane at an angle, then the line and the plane only intersect at one point. However, if the line is part of the plane, then the entire line intersects with the plane, and there are an infinite number of intersecting points.
No they can be Collinear - Points that lie on the same line.
A line and a plane that do not intersect are always skew. Skew refers to two or more lines or planes that are not parallel and do not intersect. Since a line and a plane are different-dimensional objects, they will never intersect and will always be skew.
When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.