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

Let r1 and r2 be differentiable 3-space vector-valued functions.

Show that for a differentiable 3-space vector-valued function r, the graph of r lies on a sphere centered at the origin if and only if r(t) and r′(t) are orthogonal (perpendicular) for all t.

2. Relevant equations

Dot products?

3. The attempt at a solution

If R(t) is on the surface of such a sphere then ||R(t)||=C, is constant.

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# Homework Help: Show that Vector function lies on a sphere

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