Finding where the plane intersects the x,y,z axes

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Homework Help Overview

The problem involves finding the intersection points of a plane defined by the equation x + 2y + 3z = 12 with the x, y, and z axes. The original poster mentions a point P(4,6,8) in relation to the plane.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conditions for a point to lie on the axes and question the relevance of point P in relation to the plane. There is a suggestion to express the plane's equation in intercept form to find the axis intersections.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been provided regarding the intercept form of the plane's equation, while questions about the relationship between point P and the plane remain unresolved.

Contextual Notes

There is a note that point P is not on the plane, prompting questions about whether the plane should be parallel to the original one and pass through P. The original poster expresses uncertainty about how to begin solving the problem.

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Homework Statement


The plane defined by x + 2y + 3z = 12 and the point P(4,6,8)
Find where the plane intersects the x,y and z axes

Homework Equations





The Attempt at a Solution


I don't know where to start, I can vaugely remember that the variable t is brought into the equation, but I am really stuck. Your help is appreciated.
 
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If a point (x,y,z) is on, e.g. the x-axis, what are y and z?
 
Oh, yeah, and your point P is NOT on the plane. Do you want the plane parallel to the given one and passing through P? Reread the question.
 
You can try to get the equation in the intercept form [tex]x/a+y/b+z/c=1[/tex] where (a,0,0) (0,b,0) and (0,0,c) are the intercepts on the x, y, and z axes. HINT: Divide by 12.
 

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