Evaluating surface integral (solving for unknown variables)

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Homework Help Overview

The discussion revolves around evaluating a surface integral involving multiple equations and unknown variables. Participants express confusion regarding the derivation of specific values for variables L, m, and p from the equations presented.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the derivation of five equations and question how certain values were concluded. There are mentions of obtaining a normal vector by crossing vectors along adjacent sides as a potential approach. One participant reflects on their own solution and expresses uncertainty about its applicability to more complex problems.

Discussion Status

The discussion is active, with participants sharing their thoughts and methods. Some guidance has been offered regarding the approach of finding a normal vector, and there is an acknowledgment of different interpretations of the problem. However, there is no explicit consensus on the best method yet.

Contextual Notes

Participants note that the equations may have been manipulated in ways that are not fully understood, and there is a concern about the robustness of the proposed solutions for more challenging problems.

Miike012
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The solutions have came up with 5 equations, I'm not confused how they got those 5 equations but I don't understand how it was concluded that L = 0 and m = p = 1/√2.
 

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Miike012 said:
The solutions have came up with 5 equations, I'm not confused how they got those 5 equations but I don't understand how it was concluded that L = 0 and m = p = 1/√2.

They massaged the equations somehow, who knows? The obvious way to work that problem is to get a normal vector by crossing the vectors along two adjacent sides. (Unless you see how to write the equation of the plane by inspection).
 
Nevermind, I figured it out.. But if someone has a better way please let me know.
This is my solution.
Lx + my + pz = 2p
Lx + my + pz = 2L + 2p
Lx + my + pz = 2L + 2m
Lx + my + pz = 2m
L^2 + m^2 + p^2 = 1

Then I looked at the right side of the first four equations and noticed they are all satisfied only if L = 0...
However I know this solution probably won't work for more difficult problems...
So please someone post a better solution
 
LCKurtz said:
They massaged the equations somehow, who knows? The obvious way to work that problem is to get a normal vector by crossing the vectors along two adjacent sides. (Unless you see how to write the equation of the plane by inspection).

Dang why didn't I think of that.. that's the easiest solution... just cross two vectors.. Thank you.
 

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