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karens
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Homework Statement
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.
Homework Equations
Dot products?
The Attempt at a Solution
If R(t) is on the surface of such a sphere then ||R(t)||=C, is constant.