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## Homework Statement

5. Find parametric equations for the tangent line to the curve of intersection of the surfaces

z^2 = x^2 + y^2 and x^2 + 2y^2 + z^2 = 66 at the point (3, 4, 5).

## The Attempt at a Solution

f(x,y,z) = x^2 + y^2 - z^2

g(x,y,z) = x^2 + 2y^2 + z^2

Partial derivz:

f'x = 2x

f'y = 2y

f'z = -2z

g'x = 2x

g'y = 4y

g'z = 2z

grad f = <2x,2y,-2z>

grad g = <2x,4y,2z>

grad f (3,4,5) = < 6,8,-10>

grad g (3,4,5) = <6,16,10>

then v = [(grad f) X (grad g )(cross product)

= |i j k | = 180i + 220j - 48k

|6 8 -10|

|6 16 10|

this approach is wrong because the solutions manual gives me

-10i + 4j - 2k for that vector

please help.

Thanks