# Calc 3

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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 -

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 -

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

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