Find parametric representation for the plane

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Homework Help Overview

The discussion revolves around finding a parametric representation for the plane defined by the equation 4x−2y+10z =16. Participants are exploring different parameterizations and their equivalences.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to express the variables x, y, and z in terms of parameters u and v. There are discussions about the correctness of different parameterizations and whether they are equivalent.

Discussion Status

Some participants have provided alternative parameterizations and are questioning the equivalence of their expressions. There is an acknowledgment of different approaches, but no consensus has been reached on a single correct representation.

Contextual Notes

There is a mention of a potential typo in one participant's expression, and the solutions provided in the thread suggest a specific parameterization that differs from others discussed.

dan38
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Homework Statement



Plane: 4x−2y+10z =16.

Homework Equations





The Attempt at a Solution



So I've used two parameters, "u" and "v" with x = u and y = v
Re-arranging z in terms of "u" and "v": z = 1.6 - 0.4x + 0.2y
Hence r(t) = (u , v , 1.6 - 0.4 x + 0.2y)
Is this correct?
 
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Essentially. x and y shouldn't be in your final expression; there should only be u and v.
 
oh yeah, sorry was a typo
but anyway, the solutions say the answer is (10u,10v,−4u+2v+1.6)
which isn't equivalent to my answer...
 
They're equivalent. The solutions defined the parameters as x=10u and y=10v.
 
ah I see, thanks!
 
Personally, I would have got a third answer!
We can easily solve 4x- 2y+ 10z= 16 for y: y= 2x+ 5z- 8.

Now, use x and z as parameters:
x= u
y= 2u+ 5v- 8
z= v
 

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