1. Not finding help here? Sign up for a free 30min 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!

Vector function, position and tangent vectors

  1. Sep 30, 2008 #1
    1. The problem statement, all variables and given/known data
    If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t) show that the curve lies on a sphere with center at the origin

    2. Relevant equations

    3. The attempt at a solution

    I have no idea how to even approach this problem, if somebody could give me a nudge in the right direction it would be much appreciated.
  2. jcsd
  3. Sep 30, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Differentiate r(t).r(t) (the dot product).
  4. Sep 30, 2008 #3
    Ah, I get it now.

    We know that r(t).r(t)=|r(t)|^2. Differentiating the dot product we get:

    d/dt [r(t).r(t)]= 2r'(t).r(t) = 0 (as r'(t) is orthogonal to r(t))

    thus |r(t)|^2 is constant, and so |r(t)| is constant, which corresponds to a sphere with the centre at the origin.

    Thanks Dick :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Vector function, position and tangent vectors
  1. Tangent vector (Replies: 1)

  2. Tangent vector (Replies: 1)