Search results
Math: Pre-K - 8th grade; Pre-K through grade 2 (Khan Kids) Early math review; 2nd grade; 3rd grade; 4th grade; 5th grade; 6th grade; 7th grade; 8th grade; See Pre-K - 8th Math; Math: Get ready courses; ... AP®︎/College Calculus BC; AP®︎/College Statistics; Multivariable calculus; Differential equations; Linear algebra; See all Math; Test ...
- Log In
Chętnie wyświetlilibyśmy opis, ale witryna, którą oglądasz,...
- Points, Lines, and Planes
Khan Academy
- Log In
16 sty 2023 · In both cases, to find the equation of the plane that contains those two lines, simply pick from the two lines a total of three noncollinear points (i.e. one point from one line and two points from the other), then use the technique above, as in Example 1.24, to write the equation.
A projective plane is a set of points and subsets called lines that satisfy the following four axioms: P1. Any two distinct points lie on a unique line. P2. Any two lines meet in at least one point. P3. Every line contains at least three points. P4. There exist three noncollinear points.
I understand that if I take one point or any number of collinear points, then I can draw infinite planes just by rotating around the line that connects these points, but why do we need 3 non collinear points to define a plane, why not more?
We can recall that a plane is a two-dimensional surface made up of points that extends infinitely in all directions and there exists exactly one plane through any three noncollinear points. This word, noncollinear, simply means that the three points don’t lie on a straight line.
A non-collinear point is located above or below a line. In the image below some points are above and some are below the red line. All such points are non-collinear points.
A plane, as defined by Euclid, is a “surface which lies evenly with the straight lines on itself.” A plane is a two-dimensional surface with infinite length and width, and no thickness. We also identify a plane by three noncollinear points, or points that do not lie on the same line.
