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!

Spherical vector problem

  1. Sep 24, 2005 #1
    My friends and I have been trying to work this one out all night, but to no avail.
    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 the origin.

    We know the dot product of r(t) and r'(t) = 0 or that r(t) cross r'(t) equals the multiplication of their magnitudes but to go about showing that it is a sphere because of this is causing a great deal of difficulty. Any help would be appreciated
     
  2. jcsd
  3. Sep 25, 2005 #2

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    If [itex]\vec r \cdot \frac {d \vec r}{dt} = 0[/itex] then [itex]\frac {d}{dt} r^2 = 0[/itex].
     
  4. Sep 25, 2005 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Or, to put what Tide said in different words, if the derivative of a vector is always perpendicular to the vector, the vector has constant length.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?