How would you do the following problem???
For the parametric surface r(u,v) = <u + v, u^2, v^2>, find an equation of the tangent plane at r(1,2).
evaluated at (1,2)
taking the dervitvies we get
Now taking the cross product we get
so now we need to know the point for the tangent plane
now we need a vector in the plane containing (x,y,z) so
Now if we dot the normal vector with the above generic vector they will equal zero. (why?)