If a line is known to be in a vertical plain Does the line has to be a vertical line?

No, indeed the line *could* be horizontal. A vertical plane is like the face of a wall, whiteboard or a computer screen (assuming each is actually vertical). Any combination of dots/pixels on those surfaces can be joined up in one way or another to form a line, straight, curved or angular. Because every point on that line is on the vertical plane, the line must also be on the vertical plane. It is easy then to see that a perfectly horizontal line, such as those seen bounding every box on this website, can still be part of a vertical plane. It just so happens that, in that very special case, it also belongs to another set of lines that lie on a horizontal plane.