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Find a vector function that represents the curve of intersection of the two surfaces.

The semiellipsoid $ x^2 + y^2 + 4z^2 = 4, y \ge 0 $, and the cylinder $ x^2 + z^2 = 1 $

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$\cos \theta \mathbf{i}+\sqrt{3}|\cos \theta| \mathbf{j}+\sin \theta \mathbf{k}$Where $\theta \in[0,2 \pi]$

02:09

Wen Zheng

03:14

Carson Merrill

Calculus 3

Chapter 13

Vector Functions

Section 1

Vector Functions and Space Curves

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University of Michigan - Ann Arbor

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Lectures

03:04

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].

08:32

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

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Find a vector function tha…

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Yeah. Must we consider the equation of services that are X squared plus by square? Yes ordered square equal to was Where Y is greater than equal to zero and extra square less zero is square Is equal to one. Now if we find a perimeter that satisfy all these equations so you know that thanks is equal to cause mm and said equal to sign the said despite extra square plus that describe it quite what And also we consider the other equation as why equal plus minus spare room or minus axis square minus four dead special vote is given that why is Greater than equal to zero so we can take into account that Y is equal to straddle war minus excess square minus for their square. No, we substitute X equal coast to eat their equal scientific in this. We get why we're doing spread out or minus course is square t minus four sine square the no let us simplify this. So from above we will get Y is equal to spare room war minus. Also squared the yes sign, spread G minus. See sine squared mm. No from a ball we will get Y. Is equal to spread route. See close the squares E. As why is it quoting spare a tree close mm. Is uh surfaces access granted? There's vice. Where Last four dead squared equal to four. Why is greater than equal to zero extra square Plus they're spread equal to one. Uh huh. Satisfied why parametric aggressions X. Of T. Why of the third of the equal to or steam Scared of three was mm. Sign he or in other words the vector function that satisfied the curve of intersection of their faces is R. Of P equals or ski spare a tree. Of course I. E. Sign E. So now we first draw the intersecting so this is which we can see on the screen right now. And by the help of this, the car of intersection of the surfaces is look like this. So these are the intersecting curves of the same shape with the positive and negative values, Or why?

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