(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Give a parametric representation of the plane x + y + z = 5.

2. Relevant equations

I am really not sure, I've been over the chapters we've covered for a little over an hour now, and the only mention i can find of a parametric representation of a plane is in passing once, merely stating that such a thing exists. All examples and explanations relate to

0 = a(x-x1) + b(x-x1) + c(z-z1)

where <a, b, c> is a vector normal to the plane, and (x1,y1,z1) is a point on the plane.

3. The attempt at a solution

well, I am going to assume that 0 = a(x-x1) + b(x-x1) + c(z-z1) is the standard form for planes, so I started by putting x + y + z = 5 in that form.

x + y + z = 5

x + y + z -5 = 0

i picked an arbitrary point on the plane, (2,2,1)

a(x-2) + b(y-2) + c(z-1) = 0, and therefore the coefficents must all be 1, giving me

(x-2) + (y-2) + (z-1) = 0, along with <1,1,1> being a vector normal to this plane.

i am really not sure where to go after this...

i know how to find the parametric representation of the intersection of two planes, but of the plane itself. . .

I am sorry i don't have much work to show for this, but I really have no idea where to start.

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# Homework Help: Parametric Representation of a Plane

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