Line
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yes
When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.
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.
Zero (if the line is parallel to the plane), one (generally), or an infinite number (if the line is within the plane).
A plane.