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The origin.
the very center of a coordinate plane is called the origin or (0,0) :D
A point zero dimensional can exist in a to dimensional plane because it occupies the zero point in both dimensions.
Zero (if the line is parallel to the plane), one (generally), or an infinite number (if the line is within the plane).
Take any three vectors in a plane which, when placed end-to-end form a triangle. The resultant of the three vectors will be zero.