Equation of Plane Passing Through (-1,2,1): 2x-3y+z-4=0

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Homework Help Overview

The problem involves finding the equation of a plane that passes through the point (-1, 2, 1) and contains the line of intersection of two given planes. The subject area includes vector calculus and geometry related to planes in three-dimensional space.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using normal vectors of the given planes and the cross product to find a normal vector for the desired plane. There are questions about the correctness of calculations and methods for finding the line of intersection and the direction from the point to that line.

Discussion Status

Some participants have confirmed certain approaches, while others express uncertainty about their calculations and seek clarification. There is a recognition of the need to find a vector perpendicular to the direction from the point to the line of intersection, indicating a productive exploration of the problem.

Contextual Notes

Participants note potential issues with calculations leading to discrepancies with book answers, and there is an emphasis on understanding the geometric relationships involved in the problem.

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Homework Statement


Find the equation of the plane that passes throughthe point (-1,2,1) and contains the line of intersection of the planes x+y-z=2, and 2x-y+3=1


Homework Equations


[tex]a(x-x_{o})+b(y-y_{o})+c(z-z_{o})=0[/tex]

The Attempt at a Solution


My reasoning is that we can take the normal vectors of the given planes, take the cross product, which will be orthoganol to the plane we want.
We then just plug the obtained normal vector and the point into the equation. Right?
 
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that's correct
 
Just wanted to check.
I get an anwer but it is wrong from the books, so it must be my doing.
 
put up your calculations in tex and i'll follow em through
 
Shouldn't you find the the line of intersection? And then the direction from the point (-1,2,1) to a point on the line? And then find a vector perpendicular to the two directions? And then pick any point that you know is going to be on your plane to satisfy your scalar equations?
 
ZioX said:
Shouldn't you find the the line of intersection? And then the direction from the point (-1,2,1) to a point on the line? And then find a vector perpendicular to the two directions? And then pick any point that you know is going to be on your plane to satisfy your scalar equations?

yea that's right, i wasn't thinking straight. how do you find a vector that's perpindicular to the vector that points from the (-1,2,1) to the line of intersection? find a vector which when crossed with it = 0?
 
ice109 said:
yea that's right, i wasn't thinking straight. how do you find a vector that's perpindicular to the vector that points from the (-1,2,1) to the line of intersection?

What is the angle between the cross product of two vectors and either of the two multiplicand vectors?
 
D H said:
What is the angle between the cross product of two vectors and either of the two multiplicand vectors?

90deg , yea just cross the vector from (-1,2,1) and the line of intersection to the normal vector of the plane
 

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