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Homework Help: Show that Vector function lies on a sphere

  1. May 16, 2010 #1
    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.
  2. jcsd
  3. May 16, 2010 #2


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    Homework Helper

    so, if i;m interpreting this correctly if ||r(t)||=c, then you could write it as:

    [tex] \textbf{r}(t) \bullet \textbf{r}(t) = c^2 [/tex]
    how about differentiating...

    note that as the question has "if & only if" you must show both directions, necessary & sufficient" to complete the proof
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