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A line which lies in the x-y plane might intersect the z-axis (at the origin) if it passes through the origin. In this case the line is perpendicular to the z-axis. For all other cases (where the line does not pass through the origin): those lines are skew with the z-axis (not parallel).

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Q: Why the line drawn on x-y plane is parallel to z-axis in three coordinate system?
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