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: Proving Vector Properties

  1. Jun 13, 2008 #1

    multivariable

    User Avatar

    I can't seem to figure out how to prove the property for R(t) = <f(t), g(t), h(t)> :

    Dt[R(t) X R'(t)] = R(t) X R"(t)

    Any suggestions?!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    multivariable, Jun 13, 2008
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Jun 13, 2008 #2

    lurflurf

    User Avatar
    Homework Helper

    is X cross product?
    [R(t) X R'(t)]' = R'(t) X R'(t)+R(t) X R"(t)
    for any sensible derivative
    thus
    [R(t) X R'(t)]' = R(t) X R"(t)
    if and only if
    R'(t) X R'(t)=0
    clearly true for cross product
     
    lurflurf, Jun 13, 2008
  4. Jun 13, 2008 #3

    HallsofIvy

    User Avatar
    Science Advisor

    Is the "Dt" derivative with respect to t? i.e.(R x R')' ?

    What have you tried? Have you tried actually writing out each side in terms of derivatives of f, g, and h?

    Do you know that the "product rule" from Calculus I is still true for vector products? What does that give you?
     
    HallsofIvy, Jun 13, 2008
  5. Jun 13, 2008 #4

    multivariable

    User Avatar

    wow.. I had copied the property [R(t) x R'(t)]' = blah blah blah.. incorrectly from my book... It makes perfect sense now, thank you for the help!!
     
    multivariable, Jun 13, 2008
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook