Question

Find an equation for the tangent plane to the surface given by Υ(u; v) = (u^2- v^2; u + v; u^2 + 3v)at the point (3; 1; 1).

Answer 1

http://en.wikipedia.org/wiki/Parametric_surface#Tangent_plane_and_normal_vector

Answer 2

(u^2- v^2; u + v; u^2 + 3v) = (3; 1; 1) to find the value of 'u' and 'v'
then use it to find the normal vector at given point.
now since you know normal vector and a point, you can find the equation of tangent point.

Answer 3

*plane

Answer 4

http://www.wolframalpha.com/input/?i=solve+u%5E2-+v%5E2%3D3%2C+u+%2B+v%3D1%2C+u%5E2+%2B+3v%3D1

Answer 5

http://www.wolframalpha.com/input/?i=%282u%2C+1%2C+2u%29+cross+product+%28-2v%2C+1%2C3%29