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Calculus/Cal II. Vectors
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Question
"Find a vector valued function that represents the curve C of intersection of the surface z^2=x^2+y^2 and the plane 2z= 1=y for z is greater than or equal to zero."
If 2z=y, then z=2y.
Finding the intersection with the equation z² = x² + y² can be done
by putting z=2y into it, to get 4y² = x² + y².
This means the 3y² = x². This happens when y√3 = x.
The function would be z² = 3y² + y² = 4y².
I believe a vector to describe this would be found by letting x=t.
From this, we know that y = √3t.
From both of these, we know that z = 4t².
The vector should be (t, √3t, 4t²).
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Answers by Expert:
Scotto
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