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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.
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.
-- An infinite number of different planes can intersect the same line. -- The same line can lie in an infinite number of different planes. -- An infinite number of different lines can intersect the same plane.
Two intersecting straight lines uniquely define one single plane.
A minimum of 2, but an infinite number of planes can intersect at the same line.