Equation of a Plane with 2 Points and Perpendicular

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Homework Help Overview

The problem involves determining the equation of a plane defined by two points and its perpendicularity to another plane. The subject area includes vector geometry and the properties of planes in three-dimensional space.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use one of the given points and the normal vector of the perpendicular plane to formulate the equation. Some participants question whether both points need to be incorporated into the solution.

Discussion Status

The discussion is ongoing, with participants exploring the implications of using one versus both points. There is a suggestion that the normal vector identified by the original poster may not be appropriate for the desired plane, indicating a potential misunderstanding of the problem's requirements.

Contextual Notes

Participants note a discrepancy between the original poster's derived equation and a provided answer from a textbook, raising questions about the validity of their approach and the uniqueness of the solution.

emma3001
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Homework Statement



Determine the equation of the plane that contains the points A(1, 2, 3) and B(2, 3, -1) and is perpendicular to the plane 3x + y + z + 1=0. I think I know how to do it with only one point, not two

The Attempt at a Solution



I know that v= normal so it would be (3, 1, 1). Then I could use point A and say (x-1, y-2, z-3)dot(3, 1, 1)=0
After expanding, I get 3x + y + z -8=0. Do I need to incorporate the other point?
 
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No, you only need to use one point. Notice that if you had used the other point, you would have gotten the same equation.
 
the answer in the book is 5x-13y-2z+27=0. Does it make sense that my answer is so different? Would they give the same answer?
 
Your normal vector is wrong. (3,1,1) is perpendicular to the given plane, but not the plane they want.
 

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