carlodelmundo said:Homework Statement
http://carlodm.com/images/math1.png
My question is:
Isn't it possible for two planes to have one solution? Geometrically, what if their edges were touching and that was the extent of their intersection?
carlodelmundo said:Oh. Right. I forgot that went infinite. The darn diagrams make it look like they have edges!
A linear algebra question about two planes involves finding the relationship between two planes in three-dimensional space. This can include determining if the planes are parallel, intersecting, or skew, as well as finding the point of intersection or the angle between the planes.
To determine if two planes are parallel, you can compare their normal vectors. If the normal vectors are parallel, then the planes are parallel. Another method is to find the angle between the normal vectors - if the angle is 0 or 180 degrees, the planes are parallel.
The point of intersection between two planes can be found by setting the equations of the planes equal to each other and solving for the variables. The resulting values will be the coordinates of the point of intersection.
Intersecting planes share a common point, meaning they cross each other. Skew planes, on the other hand, do not have a common point and are not parallel. They are also not intersecting, as they do not lie on the same plane.
Linear algebra can be applied to various real-life situations, such as in 3D computer graphics and animations, where planes are used to represent surfaces and objects. It is also used in physics to analyze forces and motion in three-dimensional space. Additionally, linear algebra is used in engineering and architecture to calculate the orientation and position of structures in space.