Posted by Becky on .
Find parametric equations for the tangent line to the curve of intersection of the paraboloid
z = x2 + y2
and the ellipsoid
6x2 + 5y2 + 7z2 = 39
at the point
(−1, 1, 2)

Calc 3 
Steve,
if u and v are functions of x,y,z, then the normals are
Nu = ∇u
Nv = ∇v
The tangent line of the intersection is perpendicular to both normals
T(x,y,z) = ∇u × ∇v
∇u = 2xi + 2yj  k
∇v = 12xi + 10yj + 14zk
T(1,1,2) = 33i + 34j + 2k
so that would be
x = 1 + 33t
y = 1 + 34t
z = 2 + 2t 
Calc 3 
Becky,
can you please explain to me where you got the numbers for T(1,1,2) I know you did the cross product but I can not seem to get the same numbers as you. Please explain