Please tell me the definition of this problem

  • Thread starter rado5
  • Start date
  • Tags
    Definition
In summary, the problem involves finding the unique vector perpendicular to the circle x^2+y^2=100 at the point (6,8). The solution is obtained by calculating the gradient of F(x,y)=x^2+y^2-100, or F(x,y)=x^2+y^2, and finding the unit normal. The final solution is \nablaF/\left|\nablaF\left| = (0.6,0.8).
  • #1
rado5
73
0

Homework Statement



Find the unique vector which is perpendicular on x2+y2=100 at (x0,y0)=(6,8).

Homework Equations



[tex]\nabla[/tex]F[tex]/[/tex] [tex]\left|[/tex] [tex]\nabla[/tex]F [tex]\left|[/tex]

The Attempt at a Solution



I think the solution is [tex]\nabla[/tex]F[tex]/[/tex] [tex]\left|[/tex] [tex]\nabla[/tex]F [tex]\left|[/tex] but I don't know how to calculate [tex]\nabla[/tex]F for x2+y2=100
I know [tex]\nabla[/tex]F=([tex]\partial[/tex]F[tex]/[/tex][tex]\partial[/tex]x,[tex]\partial[/tex]F[tex]/[/tex][tex]\partial[/tex]y,[tex]\partial[/tex]F[tex]/[/tex][tex]\partial[/tex]z)
Please tell me how I can find the answer. What is F here?
 
Last edited:
Physics news on Phys.org
  • #2
F(x,y)=x^2+y^2-100. The level surface is F(x,y)=0. Now do the gradient. Or F(x,y)=x^2+y^2 and the level surface is F(x,y)=100, your choice.
 
  • #3
So in this case the solution is [tex]\nabla[/tex]F[tex]/[/tex][tex]\left|[/tex][tex]\nabla[/tex]F[tex]\left|[/tex] = (0.6,0.8) Is it correct?
([tex]\nabla[/tex]F=(2x,2y)).
 
  • #4
rado5 said:
So in this case the solution is [tex]\nabla[/tex]F[tex]/[/tex][tex]\left|[/tex][tex]\nabla[/tex]F[tex]\left|[/tex] = (0.6,0.8) Is it correct?
([tex]\nabla[/tex]F=(2x,2y)).

If you mean to find the unit normal to the circle, sure, that's right.
 
  • #5
Thank you very much really. I actually translated the problem from persian to English, but I think it is now correct. Again thank you very much for your great generosity.
 

1. What is the purpose of defining a problem?

Defining a problem is important because it helps us understand and analyze the issue at hand. It also allows us to identify the root cause of the problem and develop effective solutions.

2. How do you define a problem?

To define a problem, you need to clearly state the issue or challenge, provide context and background information, and specify the goals or desired outcomes. It is also helpful to gather data and evidence to support your definition.

3. Why is problem definition considered a crucial step in the scientific method?

Problem definition is a crucial step in the scientific method because it sets the foundation for the entire research process. It helps guide the formulation of hypotheses, experimental design, and data analysis, ensuring that the research is focused and relevant.

4. Can a problem have multiple definitions?

Yes, a problem can have multiple definitions depending on the perspective or context. Different individuals or disciplines may define a problem differently based on their own understanding and objectives.

5. How can a clear problem definition lead to more effective solutions?

A clear problem definition allows for a more targeted and precise approach to finding solutions. It helps to avoid wasting time and resources on irrelevant or superficial solutions by focusing on the root cause and specific aspects of the problem.

Similar threads

  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
12
Views
2K
  • Calculus and Beyond Homework Help
Replies
11
Views
2K
Replies
1
Views
513
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
2K
  • Calculus and Beyond Homework Help
Replies
12
Views
2K
  • Calculus and Beyond Homework Help
Replies
26
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
Back
Top