Find if a Vecotr field is perpendicular to a curve

[swraman]

Homework Statement

http://math.berkeley.edu/~teleman/53f08/review2.pdf
Question #4

Homework Equations

Not sure

The Attempt at a Solution

I have no idea...
I really don't care about the answer, I have that, but I just don't know how to find out if a vector field is perpendicular to a curve.
Thanks

 

[HallsofIvy]

Do you mean perpendicular at every point on the curve? You determine whether a single vector is perpendicular to a curve at a given point by taking the dot product of the vector with the tangent vector to the curve at that point. Can you generalize that to a vector field?

 

[neo86]

If you want to find out if a vector field is perpendicular you have to check that the scalar product of the tangent vector of the curve and the Vector Field vanishes at every point of the curve.

Since you have given the curve only implicitly you would probably need implicit function theorem to actually get the tangent vector.

 

[Dick]

The easy way to get a tangent direction is to take the cross product of the normals of the surfaces defined by the two equations.