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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.
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Line–line intersection. Two intersecting lines. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection .
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 of geometric intersection include: Line–plane intersection; Line–sphere intersection; Intersection of a polyhedron with a line
Nov 17, 2020 · If they do intersect, determine whether the line is contained in the plane or intersects it in a single point. Finally, if the line intersects the plane in a single point, determine this point of intersection. Line: x = 2 − t Plane: 3x − 2y + z = 10 y = 1 + t z = 3t. Solution.
Jan 16, 2023 · Line of intersection of two planes. Figure 1.5.9: Suppose that two planes P1 and P2 with normal vectors n1 and n2, respectively, intersect in a line L. Since \textbf {n}_ {1} \times \textbf {n}_ {2} \perp \textbf {n}_ {1}, then \textbf {n}_ {1} \times \textbf {n}_ {2} is parallel to the plane P_ {1}.
In this case, P is the point of intersection of the ray and the plane - P0 is the starting point of the line - P1 is the end point of our line segment - t is the parameter. Values between 0 and 1 represent points on our line. The equation of a plane is: N dot (P – P2) = 0 - N is the normal of the plane - P and P2 are known points on the plane.
