Visualizing Tangent Vectors on a Sphere: How to Interpret Geometrically?

[Daveyboy]

Hi,

I'm trying to get an idea of what this is in my head but I do not have mathematica handy.

f:R1 to R3
|f(t)|=1
and f'(t)f(t)=0

should I just imagine these as being two tangent vectors.

 

[slider142]

If that is a dot product, you should already know of a common simple curve whose tangent lines are always perpendicular to the position vector of the curve. The fact that the length of the position vector is a constant should tell you that the curve is a subset of a particular common surface.

 

[Daveyboy]

Me thinks sphere.

 

[Pinu7]

Yous thinks right.

Well, circle I think, actually.

 

[slider142]

The sphere is the right idea. Note that the curve does not need to be a circle.