1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    lanedance

    User Avatar
    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook