Where Does a Line Meet a Plane?

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Homework Help Overview

The problem involves finding the intersection point of a line defined by parametric equations and a plane defined by a linear equation. The subject area includes vector geometry and algebraic manipulation.

Discussion Character

  • Exploratory, Problem interpretation

Approaches and Questions Raised

  • Participants discuss substituting the line's parametric equations into the plane's equation to find the value of the parameter t. There are questions about whether to find projections or directly solve for t.

Discussion Status

The discussion includes various interpretations of how to approach the problem, with some participants suggesting specific substitutions and others confirming the method of solving for t. There is no explicit consensus, but multiple lines of reasoning are being explored.

Contextual Notes

Some participants express uncertainty about the process due to a lack of recent practice with similar problems.

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Homework Statement


Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -1


Homework Equations





The Attempt at a Solution


vector of line= <1,2,-3>

Am I suppose to find the projection of the two vectors?
 
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Don't you need to find the values of t for which x+y-z=-1?

Plug x,y and z into the planes equation in terms of t, find the value of t for which the equality holds then transfer it back to the line to find the position of the intersection.
 
plug -1 into the line equation right? and that should give me the value of t?
 
I havn't done this for a while, but it looks like x+y-z=-1 means that (1+t) + 2t - (-3t) = -1 should give you t, and then you can work out the co-ordinates of this point.
 
thanks I figured it out. intersects at point (2/3, -2/3, 1)
 

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