Results 1 to 2 of 2

Math Help - Vector valued function problem

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    14

    Vector valued function problem

    "Show that, at a local max or min of ||\vec{r}(t)||, the vector r'(t) is perpendicular to \vec{r}(t)"

    I think that if f(t) = ||\vec{r}(t)||^2, then the local min/max of f(x) should be the same as ||\vec{r}(t)||, but I am not quite sure how to proceed with the rest of the question after that or how to show that r'(t) is perpendicular to \vec{r}(t).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Here are a few relevant ideas:

    1. \|\mathbf{r}(t)\|^{2}=\mathbf{r}(t)\cdot\mathbf{r}  (t)

    2. If \|\mathbf{r}(t)\| has a max or min, then \|\mathbf{r}(t)\|^{2} does as well. Proof: assume

    \dfrac{d}{dt}\|\mathbf{r}(t)\|=0.

    Then \dfrac{d}{dt}\|\mathbf{r}(t)\|^{2}=2\|\mathbf{r}(t  )\|\,\dfrac{d}{dt}\|\mathbf{r}(t)\|=0.

    QED.

    3. The product rule for derivatives works for the dot product.

    There are some hints for you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: March 16th 2011, 08:11 PM
  2. Vector Valued Function Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 18th 2009, 03:45 PM
  3. Vector-Valued Function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 10th 2008, 06:50 PM
  4. vector-valued function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 7th 2007, 09:29 AM
  5. vector valued function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 22nd 2007, 05:54 PM

Search Tags


/mathhelpforum @mathhelpforum