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.
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 ...
The line of intersection between two planes ... so insert this equation into each of the equations of the planes to get two simultaneous equations which can be ...
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...
Alternatively, a line can be described as the intersection of two planes. Let L be a line contained in distinct planes a and b with homogeneous coefficients (a 0 : a 1 : a 2 : a 3) and (b 0 : b 1 : b 2 : b 3), respectively. (The first plane equation is =, for example.)
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 distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line y = − x / m . {\displaystyle y=-x/m\,.} This distance can be found by first solving the linear systems
It may be worth mentioning here that the line of intersection of two planes consists of the set of fixed points, hence the rotation axis, of a coordinate rotation that maps one plane onto the other. For the New York to Paris example the results are: