(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a curve has the property that the position vectorr(t) is always perpendicular to the tangent vectorr'(t), show that the curve lies on the sphere with center at the origin.

2. Relevant equations

I know dot product might help:

r(t) .r'(t) = 0

and the equation of a sphere in 3-space:

r^{2}= x^{2}+ y^{2}+ z^{2}

3. The attempt at a solution

if I write out the components of the dot product...

r(t) .r'(t) = f_{x}(t)*f_{x}'(t) + f_{y}(t)*f_{y}'(t) + f_{z}(t)*f_{z}'(t) = 0

From there, I am not sure what to do, if that even is the right way to start.

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# Homework Help: Vector-valued function tangent

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