[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 vectors i + j + - k and i - 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 + - k and b = i - j + k which 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 + k and 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.