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math_proof
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is this vector field F tangent to or normal to the curve C
 one year ago
 one year ago
math_proof Group Title
is this vector field F tangent to or normal to the curve C
 one year ago
 one year ago

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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>
 one year ago

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

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

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

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

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

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

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

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

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

eseidl Group TitleBest ResponseYou've already chosen the best response.1
no prob...been awhile since I've done these
 one year ago
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