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2. Plane–plane intersection - Wikipedia

   en.wikipedia.org/wiki/Plane–plane_intersection

   This is found by noticing that the line must be perpendicular to both plane normals, and so parallel to their cross product (this cross product is zero if and only if the planes are parallel, and are therefore non-intersecting or entirely coincident).

3. Intersection (geometry) - Wikipedia

   en.wikipedia.org/wiki/Intersection_(geometry)

   The intersection points are: (−0.8587, 0.7374, −0.6332), (0.8587, 0.7374, 0.6332). A line–sphere intersection is a simple special case. Like the case of a line and a plane, the intersection of a curve and a surface in general position consists of discrete points, but a curve may be partly or totally contained in a surface.

4. Concurrent lines - Wikipedia

   en.wikipedia.org/wiki/Concurrent_lines

   The two bimedians of a quadrilateral (segments joining midpoints of opposite sides) and the line segment joining the midpoints of the diagonals are concurrent and are all bisected by their point of intersection. [3]: p.125 In a tangential quadrilateral, the four angle bisectors concur at the center of the incircle. [4]

5. Intersection curve - Wikipedia

   en.wikipedia.org/wiki/Intersection_curve

   In the simplest case, the intersection of two non-parallel planes in Euclidean 3-space is a line. In general, an intersection curve consists of the common points of two transversally intersecting surfaces, meaning that at any common point the surface normals are not parallel. This restriction excludes cases where the surfaces are touching or ...

6. Plane (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Plane_(mathematics)

   In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...

7. Hyperplane - Wikipedia

   en.wikipedia.org/wiki/Hyperplane

   In geometry, a hyperplane of an n-dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V.The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can ...

8. Transversal (geometry) - Wikipedia

   en.wikipedia.org/wiki/Transversal_(geometry)

   Unlike the two-dimensional (plane) case, transversals are not guaranteed to exist for sets of more than two lines. In Euclidean 3-space, a regulus is a set of skew lines , R , such that through each point on each line of R , there passes a transversal of R and through each point of a transversal of R there passes a line of R .

9. Point–line–plane postulate - Wikipedia

   en.wikipedia.org/wiki/Point–line–plane_postulate

   Intersecting planes assumption. If two different planes have a point in common, then their intersection is a line. The first three assumptions of the postulate, as given above, are used in the axiomatic formulation of the Euclidean plane in the secondary school geometry curriculum of the University of Chicago School Mathematics Project (UCSMP).