(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Parametric Surfaces and Their Areas

Hello,

I am having problems visualizing a concept. First I will post my question as it is given in Jame's Stewart's Fourth Edition Multivariable Calculus text, Chapter 17, section 6, question 17.

Find a parametric representation for the given surface.

(a) The plane that passes through the point (1,2,-3) and contains the two vectorsi + j + - kandi - j + k.

Now I know that vector representation in the solution can be written as

r(u,v) = rsub0 + ua + vb

where a =i + j + - kand b =i - j + kwhich becomes

r(u,v) = <1,2,-3> + u<1,1,-1> + v<1,-1,1>

which would produce parametric equations

x = 1 + u + v,

y = 2 + u -v,

z = -3 -u + v.

But what I am wondering what if I let a =i - j + kand b =i + j + - k. Then I would have

r(u,v) = <1,2,-3> + u<1,-1,1> + v<1,1,-1>

which would produce different parametric equations than the first.

x = 1 + u + v,

y = 2 - u + v,

z = -3 + u - v.

Now intuitively I think this is just as valid as the first. Is it though?

Any help / input is appreciated. Thankyou.

I'm back and the more I think about it and fool around with it I believe it is not possible to have two vector equations representing a plane with the above criteria. If that is the case then how do I determine which vector is multiplied by the parameter u and which vector is multiplied by the parameter v? This is the part that is confusing me.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Parametric Surfaces and Their Areas

**Physics Forums | Science Articles, Homework Help, Discussion**