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In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
Since these are equivalent properties, any one of them could be taken as the definition of parallel lines in Euclidean space, but the first and third properties involve measurement, and so, are "more complicated" than the second. Thus, the second property is the one usually chosen as the defining property of parallel lines in Euclidean geometry ...
After the first three points have been chosen, the fourth point will define a non-skew line if, and only if, it is coplanar with the first three points. However, the plane through the first three points forms a subset of measure zero of the cube, and the probability that the fourth point lies on this plane is zero.
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.
This geometry is preferred because it aligns σ C-H and σ* C-X orbitals. [8] [9] Figure 9 shows the σ C-H orbital and the σ* C-X orbital parallel to each other, allowing the σ C-H orbital to donate into the σ* C-X anti-bonding orbital through hyperconjugation. This serves to weaken C-H and C-X bond, both of which are broken in an E 2 reaction.
Projective geometry is an elementary non-metrical form of geometry, meaning that it does not ... and in which a "horizon" of directions corresponding to coplanar ...
For any line R and any point P which does not lie on R, in the plane containing line R and point P there are at least two distinct lines through P that do not intersect R. This implies that there are through P an infinite number of coplanar lines that do not intersect R. These non-intersecting lines are divided into two classes:
For 4 coplanar points, if one of the four points is inside the triangle formed by the other three points, then the geometric median is that point. Otherwise, the four points form a convex quadrilateral and the geometric median is the crossing point of the diagonals of the quadrilateral.