Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

math_proof

  • 2 years ago

is this vector field F tangent to or normal to the curve C

  • This Question is Closed
  1. math_proof
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    F=<y,-x> where C={(x,y):x^2+y^2=1} and n=<x,y>

  2. math_proof
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    n is a normal to C

  3. math_proof
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think is tangent but i'm not sure

  4. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Take the dot product of the normal vector and F: \[<y, -x>*<x,y>=xy-xy=0\]Since the vectors are orthogonal, the vector field cannot be normal to the curve (if it was, F and n would be parallel). Since your only other choice is parallel, they are parallel.

  5. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I mean tangent...lol

  6. math_proof
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so its normal at all points to C?

  7. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Another way to see this is to note that C is just a unit circle:|dw:1353383917635:dw|No, F is tangent to all point of C

  8. math_proof
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea C is only circle and the vector F goes in circles so that means its tangent at all points on C?

  9. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    F is tangent because it is orthogonal to the normal vector n.

  10. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353384188503:dw|

  11. math_proof
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what if F=<Y,x> and n=<x,y>

  12. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The only way F can be perpendicular to n is if F is tangent to the circle. We showed they are perpendicular because their dot product is zero. Thus F is tangent to C.

  13. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The F and n would not be orthogonal since their dot product=2xy. |dw:1353384419533:dw|They would look something like this

  14. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    However, when either x=0 or y=0 the dot product is zero and so n and F would be perpendicular at those points (F would be tangent to C at these points)...but in general 2xy doesn't equal zero so F wouldn't be tangent or normal to C at those points.

  15. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    When x=y then F=n; the vectors are parallel when x=y.

  16. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353385035892:dw|

  17. math_proof
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks a lot for that explanation

  18. eseidl
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no prob...been awhile since I've done these

  19. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.