Search results
Results from the WOW.Com Content Network
In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is the empty set if the line is parallel to the plane but outside it. Otherwise, the line cuts through the plane at a single point.
The three possible plane-line relationships in three dimensions. (Shown in each case is only a portion of the plane, which extends infinitely far.) In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is ...
The line at infinity is added to the real plane. This completes the plane, because now parallel lines intersect at a point which lies on the line at infinity. Also, if any pair of lines do not intersect at a point on the line, then the pair of lines are parallel. Every line intersects the line at infinity at some point. The point at which the ...
The Line Item Veto Act Pub. L. 104–130 (text) was a federal law of the United States that granted the President the power to line-item veto budget bills passed by Congress, but its effect was brief as the act was soon ruled unconstitutional by the Supreme Court in Clinton v. City of New York. [1]
For a hexagon with vertices lying on a conic we have the Pascal line and, in the special case where the conic is a pair of lines, we have the Pappus line. Parallel lines are lines in the same plane that never cross. Intersecting lines share a single point in common. Coincidental lines coincide with each other—every point that is on either one ...
A necessary condition for two lines to intersect is that they are in the same plane—that is, are not skew lines. Satisfaction of this condition is equivalent to the tetrahedron with vertices at two of the points on one line and two of the points on the other line being degenerate in the sense of having zero volume.
The question of the existence of an ordinary line can also be posed for points in the real projective plane RP 2 instead of the Euclidean plane.The projective plane can be formed from the Euclidean plane by adding extra points "at infinity" where lines that are parallel in the Euclidean plane intersect each other, and by adding a single line "at infinity" containing all the added points.
Lines on the plane when z = 0 are ideal points. The plane at z = 0 is the line at infinity. The homogeneous point (0, 0, 0) is where all the real points go when you're looking at the plane from an infinite distance, a line on the z = 0 plane is where parallel lines intersect.