The vector function is, r(t) =
Given two surfaces for which the vector function corresponding to the intersection of the two need to be found.
First surface is the paraboloid,
Second equation is of the parabolic cylinder,
Now to find the intersection of these surfaces, we change these equations into its parametrical representations.
Let x = t
Then, from the equation of parabolic cylinder, .
Now substituting x and y into the equation of the paraboloid, we get,
Now the vector function, r(t) = <x, y, z>
So r(t) =
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