Another Representing a curve with a vector valued function

In summary, we are finding a vector-valued function to represent the curve of intersection between two surfaces: z=y^6 and x=z^(1/3), and z=e^x and x=y^4. After solving, the potential solutions are r(t)=ti+t^(1/2)j+t^3k and r(t)=ti+t^(1/4)j+etk. Further constraints may be needed to ensure accurate representation of the curve.
  • #1
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Another ...Representing a curve with a vector valued function

Homework Statement



Find the vector-valued function that represents the curve of intersection between the following surfaces:

1) z=y6 , x=z1/3

2) z=ex , x=y4



Homework Equations





The Attempt at a Solution



Attached my work

I don't have any answers for these so I'm hoping someone can check my work? It seemed almost too easy.

Answers I got

1) r(t)=ti+t1/2j+t3k
2) r(t)=ti+t1/4j+etk
 

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  • #2


first one looks reasonable, but you might want to put some constraints on t, think about the allowable values of z for the first surface
 

FAQ: Another Representing a curve with a vector valued function

1. What is a vector valued function?

A vector valued function is a mathematical function that maps a set of input values to a set of output values, where both the input and output values are vectors. In other words, it takes in a vector as input and produces a vector as output.

2. How is a curve represented with a vector valued function?

A curve can be represented with a vector valued function by assigning a vector to each point along the curve. The vector values can represent the direction and magnitude of the curve at that particular point.

3. What are some advantages of representing a curve with a vector valued function?

One advantage of representing a curve with a vector valued function is that it allows for a more compact and efficient representation of complex curves. It also allows for easier manipulation and analysis of the curve using vector operations.

4. Can a vector valued function represent any type of curve?

Yes, a vector valued function can represent any type of curve as long as the curve can be described by a set of input and output vectors. This includes both simple and complex curves, such as straight lines, circles, or spirals.

5. Are there any limitations to representing a curve with a vector valued function?

One limitation of representing a curve with a vector valued function is that it may not be suitable for curves that are discontinuous or have sharp corners. In these cases, other mathematical representations, such as parametric equations, may be more appropriate.

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