What is the Maximum Inclination of a 3D Plane and its Equation in the XY Plane?

  • Context: MHB 
  • Thread starter Thread starter cptolemy
  • Start date Start date
  • Tags Tags
    Max Plane
Click For Summary
SUMMARY

The maximum inclination of a 3D plane represented by the equation Ax + By + Cz = 0 is achieved by a plane that is perpendicular to the reference plane. This perpendicular relationship implies that if the slope of the intersection line is denoted as m, the slope of the line representing maximum inclination is calculated as -1/m. In cases where the slope m equals zero, indicating a horizontal line, the corresponding perpendicular line is vertical and does not possess a defined slope.

PREREQUISITES
  • Understanding of 3D plane equations (Ax + By + Cz = 0)
  • Knowledge of line slopes and their geometric interpretations
  • Familiarity with the concept of perpendicular lines in geometry
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the properties of 3D planes and their equations
  • Learn about the geometric interpretation of slopes and angles
  • Explore the concept of perpendicularity in higher dimensions
  • Investigate applications of inclination in physics and engineering
USEFUL FOR

Mathematicians, physics students, and engineers who require a deeper understanding of 3D geometry and the relationships between planes and lines.

cptolemy
Messages
45
Reaction score
1
Hi,

If I have a 3D plane Ax+By+Cz=0, and I know the line equation of its intersection with the reference plane, what is the maximum inclination a point can have and what is its equation in the xy plane?

Is it perpendicular to the intersection? That is , if the slope of the intersection line is m, the max will be given by the line with a slope of -1/m?

This is embarassing...

Cheers,

Kepler
 
Physics news on Phys.org
If I understand what you mean by "inclination" then, yes, the plane with maximum "inclination" to a given plane is perpendicular to it. And, yes, if a line is perpendicular to a line with (non-zero) slope m, then it has slope -1/m. Note that if m= 0, so "horizontal", then the perpendicular line is "vertical" and does not have a defined slope.
 

Similar threads

Graduate Projection of a point from one plane onto another
  • · Replies 7 ·
Replies
7
Views
3K
MHB Vectors in Planes: Solving for m & n, Finding Orthogonal Plane
  • · Replies 2 ·
Replies
2
Views
2K
MHB Find the equation of the plane given a point and two planes
  • · Replies 1 ·
Replies
1
Views
3K
MHB Plane parallel to the xy plane?
  • · Replies 6 ·
Replies
6
Views
21K
High School Before understanding theorems in elementary Euclidean plane geometry
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Rotating Plane Point to xy Plane - CPtolemy
  • · Replies 1 ·
Replies
1
Views
2K
High School Invariant under rotation: Banal, obvious, or noteworthy?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Understanding Newton's 2nd Law for a Ball Thrown Up an Inclined Plane
  • · Replies 5 ·
Replies
5
Views
14K
Is (y + z)x1 = (y1 + z1)x the equation of a straight line in 3D space?
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad Three equations of planes, dimension should be 1?
  • · Replies 10 ·
Replies
10
Views
2K