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

  • Thread starter Thread starter cptolemy
  • Start date Start date
  • Tags Tags
    Max Plane
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
 
Mathematics 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.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

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

Hot Threads

Recent Insights

Back
Top