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2. Linear algebra - Wikipedia

   en.wikipedia.org/wiki/Linear_algebra

   In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:

3. Point–line–plane postulate - Wikipedia

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

   Number line assumption. Every line is a set of points which can be put into a one-to-one correspondence with the real numbers. Any point can correspond with 0 (zero) and any other point can correspond with 1 (one). Dimension assumption. Given a line in a plane, there exists at least one point in the plane that is not on the line. Given a plane ...

4. Intersection (geometry) - Wikipedia

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

   This proves that all points in the intersection are the same distance from the point E in the plane P, in other words all points in the intersection lie on a circle C with center E. [5] This proves that the intersection of P and S is contained in C. Note that OE is the axis of the circle. Now consider a point D of the circle C. Since C lies in ...

5. Plane-based geometric algebra - Wikipedia

   en.wikipedia.org/wiki/Plane-based_geometric_algebra

   In Plane-based GA, grade-1 elements are planes and can be used to perform planar reflections; grade-2 elements are lines and can be used to perform "line reflections"; grade-3 elements are points and can be used to perform "point reflections".

6. Arrangement of lines - Wikipedia

   en.wikipedia.org/wiki/Arrangement_of_lines

   Each line produces three possibilities per point: the point can be in one of the two open half-planes on either side of the line, or it can be on the line. Two points can be considered to be equivalent if they have the same classification with respect to all of the lines.

7. Intersection - Wikipedia

   en.wikipedia.org/wiki/Intersection

   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 ...