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Given the curve $C$, $C = {(x,y):x^2+y^2=1}$, $n=\langle x,y\rangle$ is normal to $C$.

Consider the vector field $F$ defined by $F=\langle y,-x\rangle$.

Is the vector field $F$ tangent to $C$ or normal to $C$ at points on $C$?

  • 0
    What happens at $(1,0)$?2012-11-20
  • 0
    what do you mean?2012-11-20
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    the vectors are orthogonal but I don't get it since shows vectors that go in the circle style2012-11-20
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    Draw the vector field $F$ and it becomes obvious.2012-11-20
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    If $n$ is normal to $C$, and also $F$ is orthogonal to $n$, then $F$ is "normal to the normal", making it actually tangent (in dimension 2).2012-11-20

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