Distance between Point & Plane in Vector Calculus

Click For Summary

Homework Help Overview

The discussion revolves around finding the distance between a point in three-dimensional space and a plane defined by the equation Ax + By + Cz = D. Participants are exploring various methods and concepts related to vector calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use parametric equations and cross products but is struggling to find a solution. Some participants suggest finding a vector perpendicular to the plane and a line through the point that is also perpendicular to the plane. Others introduce an alternative plane equation involving the normal vector and question how to derive the normal from the original equation.

Discussion Status

The discussion is active, with participants providing different perspectives and approaches to the problem. There is no explicit consensus, but several lines of reasoning are being explored, indicating a productive exchange of ideas.

Contextual Notes

Participants are questioning the relevance of the topic to vector calculus, suggesting a need for clarification on the tutorial's focus.

fanizza2
Messages
1
Reaction score
0
I have a point in (x,y,z) and a plane in the form Ax+By+Cz=D and I need to find the distance between the point and the plane. I tried using parametrics and cross products, but I couldn't figure it out. Thanks
 
Physics news on Phys.org
Can you find a vector that is perpendicular to the plane?
Once you have that, can you find a line that is perpendicular to the plane, and goes through the point?
 
the plane equation N.P-D=0 may be more usefull to you where N is the normal of the play. and D=N.P0, p0 a point given on the plane. Think how you'd get N from the equation you gave.
 
how exactly is this a vector calculus tutorial?
 

Similar threads

Replies
7
Views
2K
Replies
17
Views
3K
Replies
8
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
10
Views
3K
Replies
20
Views
4K
  • · Replies 3 ·
Replies
3
Views
7K
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K