Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
math_proof
Group Title
is this vector field F tangent to or normal to the curve C
 2 years ago
 2 years ago
math_proof Group Title
is this vector field F tangent to or normal to the curve C
 2 years ago
 2 years ago

This Question is Closed

math_proof Group TitleBest ResponseYou've already chosen the best response.0
F=<y,x> where C={(x,y):x^2+y^2=1} and n=<x,y>
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
n is a normal to C
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
i think is tangent but i'm not sure
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
Take the dot product of the normal vector and F: \[<y, x>*<x,y>=xyxy=0\]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.
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
I mean tangent...lol
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
so its normal at all points to C?
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
Another way to see this is to note that C is just a unit circle:dw:1353383917635:dwNo, F is tangent to all point of C
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
yea C is only circle and the vector F goes in circles so that means its tangent at all points on C?
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
F is tangent because it is orthogonal to the normal vector n.
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
dw:1353384188503:dw
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
what if F=<Y,x> and n=<x,y>
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.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.
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
The F and n would not be orthogonal since their dot product=2xy. dw:1353384419533:dwThey would look something like this
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.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.
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
When x=y then F=n; the vectors are parallel when x=y.
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
dw:1353385035892:dw
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
thanks a lot for that explanation
 2 years ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
no prob...been awhile since I've done these
 2 years ago
See more questions >>>
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
 Engagement 19 Mad Hatter
 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.